Weight of 3-paths in sparse plane graphs

zbMath1323.05058MaRDI QIDQ888584

Valerii A. Aksenov, Anna O. Ivanova, Oleg V. Borodin

Publication date: 2 November 2015

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p28

zbMATH Keywords

girthplanar graphweight3-path

Mathematics Subject Classification ID

Paths and cycles (05C38) Planar graphs; geometric and topological aspects of graph theory (05C10) Signed and weighted graphs (05C22) Density (toughness, etc.) (05C42)

Related Items (17)

All tight descriptions of 3-paths in plane graphs with girth at least 9 ⋮ All tight descriptions of 4-paths in 3-polytopes with minimum degree 5 ⋮ An analogue of Franklin's theorem ⋮ Light subgraphs in graphs with average degree at most four ⋮ Low 5-stars in normal plane maps with minimum degree 5 ⋮ 3-vertices with fewest 2-neighbors in plane graphs with no long paths of 2-vertices ⋮ Light 3-stars in sparse plane graphs ⋮ Describing neighborhoods of 5-vertices in 3-polytopes with minimum degree 5 and without vertices of degrees from 7 to 11 ⋮ All tight descriptions of 3-paths in plane graphs with girth at least 7 ⋮ All tight descriptions of 3-paths in plane graphs with girth 8 ⋮ Optimal unavoidable sets of types of 3-paths for planar graphs of given girth ⋮ An extension of Franklin's theorem ⋮ Soft 3-stars in sparse plane graphs ⋮ A tight description of 3-polytopes by their major 3-paths ⋮ Every triangulated 3-polytope of minimum degree 4 has a 4-path of weight at most 27 ⋮ All tight descriptions of major 3-paths in 3-polytopes without 3-vertices ⋮ All one-term tight descriptions of 3-paths in normal plane maps without \(K_4 - e\)

Cites Work

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• Quelques consequences simples de la formule d'Euler
• On the total coloring of planar graphs.
• Minimal vertex degree sum of a 3-path in plane maps
• Paths with restricted degrees of their vertices in planar graphs

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