منابع مشابه
Constructions of k-critical P5-free graphs
4 With respect to a class C of graphs, a graph G ∈ C is said to be k-critical if every proper 5 subgraph of G belonging to C is k−1 colorable. We construct an infinite set of k-critical P56 free graphs for every k ≥ 5. We also prove that there are exactly eight 5-critical {P5, C5}-free 7 graphs. 8
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We use the modular decomposition to give O(n(m + n)) algorithms for finding a maximum weighted clique (respectively stable set) and an approximate weighted colouring (respectively partition into cliques) in a (P5, P5)-free graph. As a by-product, we obtain an O(m+n) algorithm for finding a minimum weighted transversal of the C5 in a (P5, P5)free graph.
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A graph is (P5,gem)-free, when it does not contain P5 (an induced path with five vertices) or a gem (a graph formed by making an universal vertex adjacent to each of the four vertices of the induced path P4) as an induced subgraph. We present O(n2) time recognition algorithms for chordal gem-free and for (P5,gem)free graphs. Using a characterization of (P5,gem)-free graphs by their prime graphs...
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A bipartite graph is chordal bipartite if every cycle of length at least 6 has a chord in it. In this paper, we investigate the structure of $P_5$-free chordal bipartite graphs and show that these graphs have a Nested Neighborhood Ordering, a special ordering among its vertices. Further, using this ordering, we present polynomial-time algorithms for classical problems such as Hamiltonian cycle ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.05.018