The path partition conjecture is true for claw-free graphs

DOI10.1016/j.disc.2005.11.065zbMath1121.05092OpenAlexW2035713312WikidataQ123283230 ScholiaQ123283230MaRDI QIDQ878616

Marietjie Frick, Jean E. Dunbar

Publication date: 26 April 2007

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

Full work available at URL: https://doi.org/10.1016/j.disc.2005.11.065

zbMATH Keywords

claw-free graphslongest pathpath partition conjecturedetour order

Mathematics Subject Classification ID

Paths and cycles (05C38) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

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Path partitioning planar graphs of girth 4 without adjacent short cycles ⋮ Vertex-disjoint subgraphs with high degree sums ⋮ On the existence of vertex-disjoint subgraphs with high degree sum ⋮ Cycles in \(k\)-traceable oriented graphs ⋮ Path partitioning planar graphs with restrictions on short cycles ⋮ A note on a cycle partition problem ⋮ A note on path kernels and partitions ⋮ On a cycle partition problem ⋮ Cycle partition of two-connected and two-edge connected graphs ⋮ A note on the path Kernel conjecture ⋮ My Top 10 Graph Theory Conjectures and Open Problems ⋮ On a tree-partition problem

Cites Work

• On a closure concept in claw-free graphs
• Path partitions and \(P_{n}\)-free sets
• Graphs with not all possible path-kernels
• A survey of hereditary properties of graphs
• Partition problems and kernels of graphs
• A path(ological) partition problem
• Closure and stable Hamiltonian properties in claw-free graphs
• Detour Chromatic Numbers
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