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Total colorings-a survey (Q6152623)

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scientific article; zbMATH DE number 7815947

Language	Label	Description	Also known as
English	Total colorings-a survey	scientific article; zbMATH DE number 7815947

Statements

scholarly article

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Total colorings-a survey (English)

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Narayanan Narayanan

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Kanagasabapathi Somasundaram

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AKCE International Journal of Graphs and Combinatorics

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publication date

12 March 2024

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full work available at URL

https://arxiv.org/abs/1812.05833

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zbMATH Keywords

total coloring

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survey

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planar graph

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product graphs

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non-planar graphs

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MaRDI profile type

MaRDI publication profile

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Edge and total coloring of interval graphs

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Planar graphs with $\Delta\geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable

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Colorings of plane graphs: a survey

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List Edge-Coloring and Total Coloring in Graphs of Low Treewidth

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Total coloring of planar graphs without chordal 7-cycles

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Total coloring of planar graphs without short cycles

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Planar graphs with maximum degree 8 and without intersecting chordal 4-cycles are 9-totally colorable

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The total-chromatic number of some families of snarks

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The total chromatic number of split-indifference graphs

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Coloração Total do C²n

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The total chromatic number of some bipartite graphs

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A result on the total colouring of powers of cycles

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A note on Goldberg's conjecture on total chromatic numbers

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Special classes of snarks

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Local condition for planar graphs of maximum degree 7 to be 8-totally colorable

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Total colorings of planar graphs with maximum degree 8 and without 5-cycles with two chords

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Total colorings of \(F_5\)-free planar graphs with maximum degree 8

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Total colorings of planar graphs with sparse triangles

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Total-coloring of sparse graphs with maximum degree 6

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Total colorings of equibipartite graphs

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Total chromatic number of generalized Mycielski graphs

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The Total Chromatic Number of Graphs of High Minimum Degree

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Total chromatic number of regular graphs of odd order and high degree

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Equitable total coloring of \(C_m\square C_n\)

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An introduction to the discharging method via graph coloring

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A note on total colorings of 1-planar graphs

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Determining equitable total chromatic number for infinite classes of complete \(r\)-partite graphs

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Equitable total coloring of complete $r$-partite $p$-balanced graphs

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The total chromatic number of complete multipartite graphs with low deficiency

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Total-colorings of complete multipartite graphs using amalgamations

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On the equitable total chromatic number of cubic graphs

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On the total coloring of generalized Petersen graphs

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Total-chromatic number and chromatic index of dually chordal graphs

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On total and edge coloring some Kneser graphs

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LIST EDGE AND LIST TOTAL COLORINGS OF PLANAR GRAPHS WITHOUT 6-CYCLES WITH CHORD

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A concise proof for total coloring subcubic graphs

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Total coloring and total matching: polyhedra and facets

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Equitable total coloring of corona of cubic graphs

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Total colorings of product graphs

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Total colorings of circulant graphs

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Edge-coloring of multigraphs: Recoloring technique

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Total coloring of rooted path graphs

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THE EDGE-CHROHATIC NUMBER OF A CIRCULANT

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A total-chromatic number analogue of Plantholt's theorem

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The total chromatic number of graphs having large maximum degree

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Coloring Hanoi and Sierpiński graphs

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Total coloring of planar graphs without 6-cycles

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Total coloring of embedded graphs of maximum degree at least ten

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Total colorings of planar graphs without small cycles

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Total colorings of degenerate graphs

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Vertex-, edge-, and total-colorings of Sierpiński-like graphs

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Total and fractional total colourings of circulant graphs

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The total chromatic number of any multigraph with maximum degree five is at most seven

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Total-Coloring of Plane Graphs with Maximum Degree Nine

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A larger family of planar graphs that satisfy the total coloring conjecture

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Total chromatic number of one kind of join graphs

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Total coloring of claw-free planar graphs

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List total colorings of planar graphs without triangles at small distance

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Sufficient conditions for a planar graph to be list edge \(\Delta \)-colorable and list totally \((\Delta +1)\)-colorable

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Complexity separating classes for edge-colouring and total-colouring

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Chromatic index of graphs with no cycle with a unique chord

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Total chromatic number of {square,unichord}-free graphs

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Total chromatic number of unichord-free graphs

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Edge-colouring and total-colouring chordless graphs

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Complexity of colouring problems restricted to unichord-free and square, unichord-free graphs

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Total Colourings of Direct Product Graphs

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The parameterised complexity of list problems on graphs of bounded treewidth

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Total coloring of the prismatic graphs

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Total coloring of quasi-line graphs and inflated graphs

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A bound on the total chromatic number

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Sur le coloriage des graphs

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On the total and AVD-total coloring of graphs

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On total coloring of some classes of regular graphs

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On total chromatic number of direct product graphs

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Local condition for planar graphs of maximum degree 6 to be total 8-colorable

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Total coloring of planar graphs of maximum degree eight

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Graphs S(n, k) and a Variant of the Tower of Hanoi Problem

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Graph multiplication

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Determining the total colouring number is NP-hard

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On total 9-coloring planar graphs of maximum degree seven

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Total colorings of certain classes of lexicographic product graphs

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The hunting of a snark with total chromatic number 5

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Total chromatic numbers

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Total colourings of Cartesian products

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Total Colouring of New Classes of Subcubic graphs

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On the 7 total colorability of planar graphs with maximum degree 6 and without 4-cycles

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Planar graphs with maximum degree 7 and without 5-cycles are 8-totally-colorable

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On total colorings of some special 1-planar graphs

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The list edge coloring and list total coloring of planar graphs with maximum degree at least 7

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Total colorings of planar graphs without adjacent triangles

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TOTAL COLORINGS OF PLANAR GRAPHS WITH MAXIMUM DEGREE AT LEAST 7 AND WITHOUT ADJACENT 5-CYCLES

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Total coloring conjecture for certain classes of graphs

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Total coloring conjecture for vertex, edge and neighborhood corona products of graphs

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Total coloring of planar graphs with maximum degree \(7\)

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Total colorings of planar graphs with maximum degree seven and without intersecting 3-cycles

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Total colorings of planar graphs without intersecting 5-cycles

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Total colorings of planar graphs with small maximum degree

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Total colorings of planar graphs without chordal 6-cycles

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Total colorings of embedded graphs with no 3-cycles adjacent to 4-cycles

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Total coloring of planar graphs without chordal short cycles

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Total coloring of planar graphs without adjacent short cycles

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Total coloring of planar graphs without adjacent chordal 6-cycles

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Total coloring of embedded graphs with maximum degree at least seven

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List edge and list total coloring of planar graphs with maximum degree 8

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Total coloring of planar graphs with maximum degree 8

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Minimum total coloring of planar graph

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A note on the total coloring of planar graphs without adjacent 4-cycles

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A note on list edge and list total coloring of planar graphs without adjacent short cycles

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Total coloring of graphs embedded in surfaces of nonnegative Euler characteristic

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A note on the minimum total coloring of planar graphs

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Total coloring of 1-toroidal graphs with maximum degree at least 11 and no adjacent triangles

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Adjacent vertex distinguishing total colorings of outerplanar graphs

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On total chromatic number of planar graphs without 4-cycles

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Vertex distinguishing equitable total chromatic number of join graphs

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\((\Delta +1)\)-total-colorability of plane graphs of maximum degree \(\Delta\geq 6\) with neither chordal \(5\)-cycle nor chordal \(6\)-cycle

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The total chromatic number of regular graphs of even order and high degree

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The total chromatic number of regular graphs of high degree

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Total coloring of planar graphs with 7-cycles containing at most two chords

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Total coloring of planar graphs without some chordal 6-cycles

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Total colourings of graphs

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\((\Delta + 1)\)-total-colorability of plane graphs with maximum degree \(\Delta\) at least 6 and without adjacent short cycles

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List total coloring of pseudo-outerplanar graphs

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Total coloring of outer-1-planar graphs with near-independent crossings

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On total colorings of 1-planar graphs

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List edge and list total coloring of 1-planar graphs

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Total coloring of recursive maximal planar graphs

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A sufficient condition for planar graphs with maximum degree 6 to be totally 8-colorable

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Behzad-Vizing conjecture and Cartesian product graphs

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Even-power of cycles with many vertices are type 1 total colorable

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Compositions, decompositions, and conformability for total coloring on power of cycle graphs

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Identifiers

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10.1080/09728600.2023.2187960

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6152623

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