A simpler proof for vertex-pancyclicity of squares of connected claw-free graphs

作者：Tomescu Alexandru I^*

来源：Discrete Mathematics, 2012, 312(15): 2388-2391.

DOI：10.1016/j.disc.2012.03.042

• Claw-free graph
• Graph square
• Vertex-pancyclicity
• Perfect matching

We give a simpler proof of the well-known result of Matthews and Sumner stating that squares of connected claw-free graphs are vertex-pancyclic. Contrary to the previous proof, our approach does not resort to Fleischner%26apos;s result stating that, when restricted to squares of graphs, vertex-pancyclicity and Hamiltonicity are equivalent. The same proof idea already yielded that connected claw-free graphs of even order have a perfect matching, which is another result of Sumner. We conclude by observing that this proof identifies a larger collection of graphs for which the two properties in question hold.

• 出版日期2012-8-6