Chromatic numbers of quadrangulations on closed surfaces

DOI10.1002/jgt.1005zbMath0979.05034OpenAlexW2778765588MaRDI QIDQ2744570

Katsuhiro Ota, Joan P. Hutchinson, Atsuhiro Nakamoto, Seiya Negami, Dan S. Archdeacon

Publication date: 16 December 2001

Published in: Journal of Graph Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/jgt.1005

zbMATH Keywords

toruschromatic numberKlein bottleface-widthquadrangulation

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Relations of low-dimensional topology with graph theory (57M15) Coloring of graphs and hypergraphs (05C15) Graph representations (geometric and intersection representations, etc.) (05C62)

Related Items (23)

Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces ⋮ A topological classification of convex bodies ⋮ 3-colorable even embeddings on closed surfaces ⋮ Coloring Eulerian triangulations of the Klein bottle ⋮ 5-chromatic even triangulations on surfaces ⋮ 4-colorable 6-regular toroidal graphs. ⋮ Local chromatic number of quadrangulations of surfaces ⋮ On 4-chromatic Schrijver graphs: their structure, non-3-colorability, and critical edges ⋮ Coloring even-faced graphs in the torus and the Klein bottle ⋮ A genealogy of convex solids via local and global bifurcations of gradient vector fields ⋮ What is on his mind? ⋮ Choosability of toroidal graphs without short cycles ⋮ Local chromatic number and distinguishing the strength of topological obstructions ⋮ Coloring-flow duality of embedded graphs ⋮ Quadrangulations on 3-colored point sets with Steiner points and their winding numbers ⋮ Generating polyhedral quadrangulations of the projective plane ⋮ Unnamed Item ⋮ Quadrangulations and 4-color-critical graphs ⋮ Distributed coloring in sparse graphs with fewer colors ⋮ Colouring Eulerian triangulations ⋮ Coloring locally bipartite graphs on surfaces. ⋮ 5-chromatic even triangulations on the Klein bottle ⋮ Colouring quadrangulations of projective spaces

Cites Work

• Unnamed Item
• Grid minors of graphs on the torus
• The four-colour theorem
• Combinatorial structure on triangulations. I: The structure of four colorings
• The chromatic numbers of graph bundles over cycles
• Three-coloring graphs embedded on surfaces with all faces even-sided
• Separating and nonseparating disjoint homotopic cycles in graph embeddings
• Irreducible quadrangulations of the torus
• A Theorem of R. L. Brooks and a Conjecture of H. Hadwiger
• Short Proof of a Map-Colour Theorem
• Every planar map is four colorable
• Coloring graphs with fixed genus and girth
• Note on irreducible triangulations of surfaces
• 4-chromatic projective graphs
• Map-Colour Theorems

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