Coloring vertices and faces of locally planar graphs

DOI10.1007/s00373-006-0653-4zbMath1106.05038OpenAlexW1994609765MaRDI QIDQ855294

Michael O. Albertson, Bojan Mohar

Publication date: 5 January 2007

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00373-006-0653-4

zbMATH Keywords

1-embeddedvertex face coloring

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Coloring of graphs and hypergraphs (05C15)

Related Items

Dynamic list coloring of 1-planar graphs, Partially broken orientations of Eulerian plane graphs, On \((p,1)\)-total labelling of 1-planar graphs, An upper bound on the sum of powers of the degrees of simple 1-planar graphs, Entire coloring of graphs embedded in a surface of nonnegative characteristic, Light subgraphs in the family of 1-planar graphs with high minimum degree, List edge and list total coloring of 1-planar graphs, Coloring vertices and faces of maps on surfaces, Finite fields and the 1‐chromatic number of orientable surfaces, Non-1-planarity of lexicographic products of graphs, 1-Planar Graphs, On total colorings of 1-planar graphs

Cites Work

• Unnamed Item
• On the 1-chromatic number of nonorientable surfaces with large genus
• Ein 7-Farbensatz 1-einbettbarer Graphen auf der projektiven Ebene
• Five-coloring maps on surfaces
• An infinite series of surfaces with known 1-chromatic number
• A new lower bound on the number of edges in colour-critical graphs and hypergraphs
• Extending precolorings of subgraphs of locally planar graphs
• A list version of Dirac's theorem on the number of edges in colour-critical graphs
• The Independence Ratio and Genus of a Graph
• The vertex-face total chromatic number of Halin graphs
• Dirac's map-color theorem for choosability
• A new proof of the 6 color theorem
• On the vertex face total chromatic number of planar graphs
• Acyclic colouring of 1-planar graphs