Planar Hamiltonian chordal graphs are cycle extendable
نویسندگان
چکیده
منابع مشابه
Planar 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...
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A cycle C of length k is extendable if there is a cycle C′ of length k+1 with V (C) ⊂ V (C′). A graph G = (V,E) of order n is cycle extendable when every cycle C of length k < n is extendable. A chordal graph is a spider intersection graph if it admits an intersection representation which consists of subtrees of a sub-divided star (or spider). In 1990, Hendry conjectured that all hamiltonian ch...
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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...
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A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C is also formed from edges and one chord of a cycle C ′ of length one greater than C with V (C ) ⊆ V (C). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivale...
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We prove the result stated in the title (conjectured by Grünbaum), and a conjecture of Plummer that every graph which can be obtained from a 4–connected planar graph by deleting two vertices is Hamiltonian. The proofs are constructive and give rise to polynomial–time algorithms.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00505-8