On path-factor critical deleted (or covered) graphs

DOI10.1007/s00010-021-00852-4OpenAlexW3208979361MaRDI QIDQ2156074

Qiuxiang Bian, Si-zhong Zhou, Jian-Cheng Wu

Publication date: 15 July 2022

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-021-00852-4

zbMATH Keywords

connectivity\((P_{\geq 3},n)\)-factor critical covered graph\((P_{\geq 3},n)\)-factor critical deleted graphsun toughness

Mathematics Subject Classification ID

Deterministic network models in operations research (90B10) Paths and cycles (05C38) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Connectivity (05C40)

Related Items (18)

Discussion on fractional \((a, b, k)\)-critical covered graphs ⋮ Discussions on orthogonal factorizations in digraphs ⋮ A Note of Generalization of Fractional ID-factor-critical Graphs ⋮ Some results about ID-path-factor critical graphs ⋮ Forbidden restrictions and the existence of \(P_{\geq 2}\)-factor and \(P_{\geq 3}\)-factor ⋮ Path factors and neighborhoods of independent sets in graphs ⋮ Binding number and path-factor critical deleted graphs ⋮ Isolated toughness and path-factor uniform graphs. II. ⋮ Two sufficient conditions for odd \([1,b\)-factors in graphs] ⋮ Two Sufficient Conditions for Graphs to Admit Path Factors ⋮ Degree conditions for the existence of a {P₂, P₅}-factor in a graph ⋮ Sufficient conditions for graphs to have strong parity factors ⋮ Feasibility of data transmission under attack: from isolated toughness variant perspective ⋮ Sun toughness and path-factor uniform graphs ⋮ Path-factor critical covered graphs and path-factor uniform graphs ⋮ The \(A_\alpha\)-spectral radius for path-factors in graphs ⋮ Some sufficient conditions for path-factor uniform graphs ⋮ Tight isolated toughness bound for fractional \((k, n)\)-critical graphs

Cites Work

• Packing 3-vertex paths in claw-free graphs and related topics
• Component factors with large components in graphs
• Characterizations for \({\mathcal{P}}_{\geq 2}\)-factor and \({\mathcal{P}}_{\geq 3}\)-factor covered graphs
• A necessary and sufficient condition for the existence of a path factor every component of which is a path of length at least two
• Packing paths of length at least two
• Some results on path-factor critical avoidable graphs
• Path factors in subgraphs
• Some existence theorems on path factors with given properties in graphs
• Sun toughness and $P_{\geq3}$-factors in graphs
• Remarks on path factors in graphs
• Path factors of bipartite graphs
• Isolated toughness and path-factor uniform graphs
• Some results about component factors in graphs
• Partitioning vertices of 1-tough graphs into paths

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