2013
DOI: 10.1016/j.dam.2013.02.024
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On the vertex k-path cover

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Cited by 53 publications
(44 citation statements)
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“…, and so x i is a stem, whose degree is more than 2, a contradiction with Lemma 4. 4. Hence, we infer that also deg(x i ) = 2, and let y i be another neighbor of x i .…”
Section: Uniformly Dissociated Graphs With Girth At Leastmentioning
confidence: 88%
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“…, and so x i is a stem, whose degree is more than 2, a contradiction with Lemma 4. 4. Hence, we infer that also deg(x i ) = 2, and let y i be another neighbor of x i .…”
Section: Uniformly Dissociated Graphs With Girth At Leastmentioning
confidence: 88%
“…, x i,ji are leaves. Hence z i is a stem in G − N [V (M )], which has degree at least 3, a contradiction with Lemma 4 4…”
mentioning
confidence: 81%
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“…The k-path vertex cover problem was heavily studied on several types of graphs products. Already in [4] the Cartesian product of two paths, i.e. grid graphs, was considered.…”
Section: Introductionmentioning
confidence: 99%
“…Among the two parameters νk(G) and τk(G), only the latter seems to have received considerable attention in the literature . Note that a set X of vertices of a graph G is a 3‐vertex cover if and only if its complement V(G)/X is a so‐called dissociation set , that is, a set of vertices inducing a subgraph of maximum degree at most 1.…”
Section: Introductionmentioning
confidence: 99%