The saturation number for the length of degree monotone paths
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The saturation number for the length of degree monotone paths
A degree monotone path in a graph G is a path P such that the sequence of degrees of the vertices in the order in which they appear on P is monotonic. The length (number of vertices) of the longest degree monotone path in G is denoted by mp(G). This parameter, inspired by the well-known ErdősSzekeres theorem, has been studied by the authors in two earlier papers. Here we consider a saturation p...
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15 صفحه اولRamsey numbers for degree monotone paths
A path v1, v2, . . . , vm in a graph G is degree-monotone if deg(v1) ≤ deg(v2) ≤ · · · ≤ deg(vm) where deg(vi) is the degree of vi in G. Longest degree-monotone paths have been studied in several recent papers. Here we consider the Ramsey type problem for degree monotone paths. Denote by Mk(m) the minimum number M such that for all n ≥ M , in any k-edge coloring of Kn there is some 1 ≤ j ≤ k su...
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LetH be a simple graph. A graph G is called anH-saturated graph ifH is not a subgraph of G, but adding any missing edge to Gwill produce a copy of H . Denote by SAT (n,H) the set of all H-saturated graphs G with order n. Then the saturation number sat(n,H) is defined as minG∈SAT (n,H) |E(G)|, and the extremal number ex(n,H) is defined as maxG∈SAT (n,H) |E(G)|. A natural question is that of whet...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2015
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1817