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**publisher and metadata sources**).Given a graph in any of the following graph classes: trapezoid graphs, circular permutation graphs, convex graphs, Dilworth k graphs, k-polygon graphs, circular arc graphs and complements of… Continue Reading

Abstract For a graph class G and any two positive integers i and j , the Ramsey number R G ( i , j ) is the smallest positive integer such that every graph in G on at least R G ( i , j ) vertices has… Continue Reading

Modifying a given graph to obtain another graph is a well-studied problem with applications in many fields. Given two input graphs G and H, the Contractibility problem is to decide whether H can be… Continue Reading

Given two graphs G and H, we say that G contains H as an induced minor if a graph isomorphic to H can be obtained from G by a sequence of vertex deletions and edge contractions. We study the… Continue Reading

Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. In general graphs, the ratio cfvs(G)/fvs(G)… Continue Reading

Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem… Continue Reading

The k-Disjoint Paths problem, which takes as input a graph G and k pairs of specified vertices (si,ti), asks whether G contains k mutually vertex-disjoint paths Pi such that Pi connects si and ti,… Continue Reading

For any graph class $$\mathcal{H}$$H, the $$\mathcal{H}$$H-Contraction problem takes as input a graph $$G$$G and an integer $$k$$k, and asks whether there exists a graph $$H\in \mathcal{H}$$H∈H such… Continue Reading

Motivated by recent results of Mathieson and Szeider (J. Comput. Syst. Sci. 78(1): 179–191, 2012), we study two graph modification problems where the goal is to obtain a graph whose vertices satisfy… Continue Reading

Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. For a graph class \({\cal G}\), the price of… Continue Reading