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arXiv · 2412.20729

Longest Path and Cycle Transversals in Chordal Graphs

James A. Long Jr.·Kevin G. Milans·Michael C. Wigal
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Abstract

We show that if $G$ is a $n$-vertex connected chordal graph, then it admits a longest path transversal of size $O(\log^2 n)$. Under the stronger assumption of 2-connectivity, we show $G$ admits a longest cycle transversal of size $O(\log n)$. We also provide longest path and longest cycle transversals which are bounded by the leafage of the chordal graph.

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James A. Long Jr., Kevin G. Milans, Michael C. Wigal. 2024-12-30. Longest Path and Cycle Transversals in Chordal Graphs. https://arxiv.org/abs/2412.20729

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