منابع مشابه
On strictly Chordality-k graphs
Strictly Chordality-k graphs (SC k graphs) are graphs which are either cycle free or every induced cycle is exactly k, for some fixed k, k ≥ 3. Note that k = 3 and k = 4 are precisely the Chordal graphs and Chordal Bipartite graphs, respectively. In this paper, we initiate a structural and an algo-rithmic study of SC k , k ≥ 5 graphs.
متن کاملGraphs of low chordality
The chordality of an undirected graph G, which is not acyclic, is defined as the length of the longest induced cycle in it. The chordality of an acyclic graph is defined to be 0. We use Cl (l ≥ 3) to denote a cycle of length l. An induced cycle is called a hole. A hole is an odd hole if its length is odd and is an even hole otherwise. Odd-chordality of a graph is the length of the longest odd h...
متن کاملChordality Properties and Hyperbolicity on Graphs
Let G be a graph with the usual shortest-path metric. A graph is δ-hyperbolic if for every geodesic triangle T , any side of T is contained in a δ-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. In this paper we study the relation between the hyperbolicity of the graph and some chordality properties which are natural generaliz...
متن کاملChordality and 2-factors in Tough Graphs
A graph G is chordal if it contains no chordless cycle of length at least four and is k-chordal if a longest chordless cycle in G has length at most k. In this note it is proved that all 2 -tough 5-chordal graphs have a 2-factor. This result is best possible in two ways. Examples due to Chvátal show that for all > 0 there exists a ( 2 − )-tough chordal graph with no 2-factor. Furthermore, examp...
متن کاملGeneralized Chordality, Vertex Separators and Hyperbolicity on Graphs
A graph is chordal if every induced cycle has exactly three edges. A vertex separator set in a graph is a set of vertices that disconnects two vertices. A graph is δ-hyperbolic if every geodesic triangle is δ-thin. In this paper, we study the relation between vertex separator sets, certain chordality properties that generalize being chordal and the hyperbolicity of the graph. We also give a cha...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2020
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.06.028