Structure of neighborhoods of edges in planar graphs and simultaneous coloring of vertices, edges and faces

DOI10.1007/BF01208542zbMath0795.05048OpenAlexW2014586115MaRDI QIDQ1326890

Oleg V. Borodin

Publication date: 13 July 1994

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01208542

zbMATH Keywords

planar graphsfacessimultaneous coloringEuler polyhedraKotzig's theorem

Mathematics Subject Classification ID

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

Related Items (22)

The entire choosability of plane graphs ⋮ Weight of edges in normal plane maps ⋮ Plane graphs with maximum degree 9 are entirely 11-choosable ⋮ Facial list colourings of plane graphs ⋮ Light 3-stars in sparse plane graphs ⋮ Entire \((\varDelta +2)\)-colorability of plane graphs ⋮ An extension of Kotzig's theorem ⋮ On the colorings of outerplanar graphs ⋮ Refined weight of edges in normal plane maps ⋮ The entire chromatic number of graphs embedded on the torus with large maximum degree ⋮ Plane Graphs with Maximum Degree Are Entirely ‐Colorable ⋮ Describing \((d-2)\)-stars at \(d\)-vertices, \(d\leq 5\), in normal plane maps ⋮ Describing 3-paths in normal plane maps ⋮ Weight of 3-paths in sparse plane graphs ⋮ Plane graphs with \(\Delta = 7\) are entirely 10-colorable ⋮ Entire colouring of plane graphs ⋮ Weight of faces in plane maps ⋮ Improved bounds for guarding plane graphs with edges ⋮ Entire coloring of plane graph with maximum degree eleven ⋮ The entire coloring of series-parallel graphs ⋮ Improved bounds for guarding plane graphs with edges ⋮ Tight Descriptions of 3‐Paths in Normal Plane Maps

Cites Work

• A seven-color theorem on the sphere
• Quelques consequences simples de la formule d'Euler
• On the total coloring of planar graphs.
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