منابع مشابه
Pseudo-Hamiltonian-connected graphs
Given a graph G and a positive integer k, denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k. A graph G is called pseudo-k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo-k Hamiltonian-connec...
متن کاملHamiltonian-connected graphs
For a simple graph G, let NC D(G) = min{|N (u) ∪ N (v)| + d(w) : u, v, w ∈ V (G), uv 6∈ E(G), wv or wu 6∈ E(G)}. In this paper, we prove that if NC D(G) ≥ |V (G)|, then either G is Hamiltonian-connected, or G belongs to a well-characterized class of graphs. The former results by Dirac, Ore and Faudree et al. are extended. c © 2008 Published by Elsevier Ltd
متن کاملHamiltonian Connected Line Graphs
Thomassen conjectured [8] that every 4-connected line graph is hamiltonian. An hourglass is a graph isomorphic to K5−E(C), where C is a cycle of length 4 in K5. In [2], it is shown that every 4-connected line graph without an induced subgraph isomorphic to the hourglass is hamiltonian connected. In this note, we prove that every 3-connected, essentially 4-connected hourglass-free line graph is ...
متن کامل5-Connected Toroidal Graphs are Hamiltonian-Connected
The problem on the Hamiltonicity of graphs is well studied in discrete algorithm and graph theory, because of its relation to traveling salesman problem (TSP). Starting with Tutte’s result, stating that every 4-connected planar graph is Hamiltonian, several researchers have studied the Hamiltonicity of graphs on surfaces. Extending Tutte’s technique, Thomassen proved that every 4-connected plan...
متن کاملHamiltonian connectedness in 3-connected line graphs
We investigate graphs G such that the line graph L(G) is hamiltonian connected if and only if L(G) is 3-connected, and prove that if each 3-edge-cut contains an edge lying in a short cycle of G, then L(G) has the above mentioned property. Our result extends Kriesell’s recent result in [J. of Combinatorial Theory, Ser. B. 82 (2001), 306-315] that every 4-connected line graph of a claw free graph...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2008
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2007.10.018