منابع مشابه
Hamiltonian chordal graphs are not cycle extendible
In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater. We disprove this conjecture by constructing counterexamples on n vertices for any n ≥ 15. Furthermore, we show that there exist counterexamples where the ratio of the length of a non-extendible cycle to the total...
متن کاملPlanar Hamiltonian chordal graphs are cycle extendable
A cycle C in a graph G is extendible if there exists a cycle C 0 in G such that V (C) V (C 0) and jV (C 0)j = jV (C)j + 1. A graph G is cycle extendible if G contains at least one cycle and every nonhamiltonian cycle in G is extendible. A graph G is fully cycle extendible if G is cycle extendible and every vertex lies on a 3-cycle of G. G. Hendry asked if every hamiltonian chordal graph is full...
متن کامل10-Gabriel graphs are Hamiltonian
Given a set S of points in the plane, the k-Gabriel graph of S is the geometric graph with vertex set S, where pi, pj ∈ S are connected by an edge if and only if the closed disk having segment pipj as diameter contains at most k points of S \ {pi, pj}. We consider the following question: What is the minimum value of k such that the k-Gabriel graph of every point set S contains a Hamiltonian cyc...
متن کاملChordal Graphs are Fully Orientable
Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let dmin(G) (dmax(G)) denote the minimum (maximum) of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying dmin(G) 6 d 6 dmax(G). A graph G is c...
متن کاملWhen are chordal graphs also partition graphs?
A general partition graph (gpg) is an intersection graph G on a set S so that for every maximal independent set M of vertices in G, the subsets assigned to the vertices in M partition S. These graphs have been characterized by the presence of special clique covers. The Triangle Condition T for a graph G is that for any maximal independent set M and any edge uv in G M, there is a vcrtex W E M so...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2017
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2016.07.002