$K_5^-$-Subdivision in 4-Connected Graphs

DOI10.1137/18M1194973zbMath1401.05168MaRDI QIDQ4560390

Ping Zhang, Chang-hong Lu

Publication date: 12 December 2018

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

contractionconnectivityinternally disjoint paths\(K_5^-\)-subdivision

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graph minors (05C83) Connectivity (05C40)

Cites Work

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• Contractible edges in \(k\)-connected graphs with some forbidden subgraphs
• Some degree and forbidden subgraph conditions for a graph to have a \(k\)-contractible edge
• Hajos' graph-coloring conjecture: Variations and counterexamples
• \(3n-5\) edges do force a subdivision of \(K_5\)
• Some forbidden subgraph conditions for a graph to have a \(k\)-contractible edge
• Contractible edges and triangles in \(k\)-connected graphs
• A new degree sum condition for the existence of a contractible edge in a \(\kappa\)-connected graph
• Applications of Menger's graph theorem
• Homomorphism theorems for graphs
• A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs

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