2021
DOI: 10.48550/arxiv.2105.02018
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The k-path vertex cover: general bounds and chordal graphs

Abstract: For an integer k ≥ 3, a k-path vertex cover of a graph G = (V, E) is a set T ⊆ V that shares a vertex with every path subgraph of order k in G. The minimum cardinality of a k-path vertex cover is denoted by ψ k (G). We give estimates -mostly upper bounds -on ψ k (G) in terms of various parameters, including vertex degrees and the number of vertices and edges. The problem is also considered on chordal graphs and planar graphs.

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“…Recently, Bujtás et al [16] generalized the result to arbitrary graphs in terms of minimum and maximum degree.…”
Section: The K-path Vertex Cover Numbermentioning
confidence: 99%
See 4 more Smart Citations
“…Recently, Bujtás et al [16] generalized the result to arbitrary graphs in terms of minimum and maximum degree.…”
Section: The K-path Vertex Cover Numbermentioning
confidence: 99%
“…Theorem 6.7. [16] Let k and ∆ be integers with k ≥ 3 and ∆ = 2 or ∆ ≥ 4, and let G be a graph of maximum degree at most ∆. Then the following hold.…”
Section: The K-path Vertex Cover Numbermentioning
confidence: 99%
See 3 more Smart Citations