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Graph edge coloring: a survey (Q1733850)

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scientific article; zbMATH DE number 7040456

Language	Label	Description	Also known as
English	Graph edge coloring: a survey	scientific article; zbMATH DE number 7040456

Statements

scholarly article

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Graph edge coloring: a survey (English)

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Michael Stiebitz

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Graphs and Combinatorics

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publication date

21 March 2019

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zbMATH Keywords

chromatic index

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edge coloring

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adjacency lemma

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MaRDI profile type

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full work available at URL

https://doi.org/10.1007/s00373-018-1986-5

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The chromatic index of a graph whose core has maximum degree 2

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The chromatic index of a graph whose core is a cycle of order at most 13

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The chromatic index of a claw-free graph whose core has maximum degree 2

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On edge-colorings of graphs.

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On a limit of the method of Tashkinov trees for edge-colouring

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Counting edge-Kempe-equivalence classes for 3-edge-colored cubic graphs

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Chromatic index, treewidth and maximum degree

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NP-completeness of edge-colouring some restricted graphs

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Average degrees of edge-chromatic critical graphs

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Hamiltonicity of edge-chromatic critical graphs

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Colouring the petals of a graph

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Chromatic index determined by fractional chromatic index

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Vizing's 2‐Factor Conjecture Involving Large Maximum Degree

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Approximating the chromatic index of multigraphs

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Densities, Matchings, and Fractional Edge-Colorings

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A note on the size of edge-chromatic 4-critical graphs

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Regular Graphs of High Degree are 1-Factorizable

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1-factorizing regular graphs of high degree - an improved bound

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Edge-colouring seven-regular planar graphs

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Edge-colouring eight-regular planar graphs

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Subcubic Edge‐Chromatic Critical Graphs Have Many Edges

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Short Fans and the 5/6 Bound for Line Graphs

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The Hilton--Zhao Conjecture is True for Graphs with Maximum Degree 4

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Proof of the 1-factorization and Hamilton Decomposition Conjectures

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Packing six \(T\)-joins in plane graphs

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Maximum matching and a polyhedron with 0,1-vertices

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Extension from precoloured sets of edges

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Three-edge-colouring doublecross cubic graphs

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On the chromatic index of almost all graphs

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Edge-coloring of multigraphs: Recoloring technique

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Chromatic-index critical multigraphs of order 20

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On the chromatic index and the cover index of a multigraph

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List-edge-colouring planar graphs with precoloured edges

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Edge coloring multigraphs without small dense subsets

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Goldberg's conjecture is true for random multigraphs

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On characterizing Vizing's edge colouring bound

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A better than “best possible” algorithm to edge color multigraphs

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The NP-Completeness of Edge-Coloring

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Planar graphs of maximum degree six without 7-cycles are class one

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On critical graphs with chromatic index 4

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Remarks on planar edge-chromatic critical graphs

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Asymptotics of the chromatic index for multigraphs

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Vizing's 2-factor conjecture involving toughness and maximum degree conditions

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On the chromatic index of multigraphs without large triangles

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A new tool for proving Vizing's theorem

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Lower bounds on the number of edges in edge-chromatic-critical graphs with fixed maximum degrees

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Hamiltonian cycles in critical graphs with large maximum degree

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A Sufficient Condition for Edge Chromatic Critical Graphs to Be Hamiltonian—An Approach to Vizing's 2‐Factor Conjecture

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Decompositions for edge-coloring join graphs and cobipartite graphs

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Edge-colouring and total-colouring chordless graphs

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Optimal edge-colourings for a class of planar multigraphs

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Extending an edge-coloring

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On a theorem of Goldberg

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On the size of edge-coloring critical graphs with maximum degree 4

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On the average degree of critical graphs with maximum degree six

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Edge-coloring of split graphs.

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Edge coloring of planar graphs which any two short cycles are adjacent at most once

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On the $1.1$ Edge-Coloring of Multigraphs

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On the independence number of edge chromatic critical graphs

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Edge coloring regular graphs of high degree

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A Combined Logarithmic Bound on the Chromatic Index of Multigraphs

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All regular multigraphs of even order and high degree are 1-factorable

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Maximal \(k\)-edge-colorable subgraphs, Vizing's theorem, and Tuza's conjecture

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Ein Sechsfarbenproblem auf der Kugel

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The four-colour theorem

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Tutte's edge-colouring conjecture

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Excluded minors in cubic graphs

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An asymptotic approximation scheme for multigraph edge coloring

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Planar graphs of maximum degree seven are Class I

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Graph edge colouring: Tashkinov trees and Goldberg's conjecture

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On Vizing's bound for the chromatic index of a multigraph

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Combinatorial optimization. Polyhedra and efficiency (3 volumes)

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On Multi-Colourings of Cubic Graphs, and Conjectures of Fulkerson and Tutte

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On Tutte's extension of the four-colour problem

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Colouring series-parallel graphs

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A Theorem on Coloring the Lines of a Network

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Edge-colouring of joins of regular graphs. II

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Approximating Vizing's independence number conjecture

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On the algebraic theory of graph colorings

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A conjecture on triangles of graphs

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An Asymptotic Version of the Multigraph 1‐Factorization Conjecture

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SOME UNSOLVED PROBLEMS IN GRAPH THEORY

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Edge coloring of graphs embedded in a surface of nonnegative characteristic

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A sufficient condition for a plane graph with maximum degree 6 to be class 1

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The average degree of an edge‐chromatic critical graph II

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The independence number of an edge-chromatic critical graph

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Edge colorings of planar graphs without 5-cycles with two chords

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Every planar graph with maximum degree 7 is of class 1

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Some sufficient conditions for 1-planar graphs to be class 1

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Edge coloring of planar graphs without adjacent 7-cycles

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The edge chromatic number of outer-1-planar graphs

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On edge colorings of 1-planar graphs without adjacent triangles

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On edge colorings of \(1\)-planar graphs

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On the chromatic index of join graphs and triangle-free graphs with large maximum degree

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S00373-018-1986-5

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Sitelinks

Mathematics(1 entry)

mardi Publication:1733850

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