Articles

Dirac type condition and Hamiltonian-connected graphs

Published in: Quaestiones Mathematicae
Volume 34, issue 4, 2011 , pages: 521–525
DOI: 10.2989/16073606.2011.640768
Author(s): Deqin ChenDepartment of Mathematics, China, Zu LiDepartment of Mathematics, China, Kewen Zhao*Department of Mathematics, China

Abstract

In 1952 Dirac introduced the Dirac type condition and proved that if G is a connected graph of order n ≥ 3 such that δ(G) ≥ n/2, then G is Hamiltonian. In this paper we consider Hamiltonian-connectedness, which extends the Hamiltonian graphs and prove that if G is a connected graph of order n ≥ 3 such that δ(G) ≥ (n −1)/2, then G is Hamiltonian-connected or G belongs to five families of well-structured graphs. Thus, the condition and the result generalize the above condition and results of Dirac, respectively.

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