When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

This article is intended as a survey, updating earlier surveys in the area. For completeness
of the presentation of both particular questions and the general area, it also contains …

In this survey we have attempted to bring together most of the results and papers that deal
with toughness related to cycle structure. We begin with a brief introduction and a section on …

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On some intriguing problems in hamiltonian graph theory—a survey Page 1 Discrete
Mathematics 251 (2002) 47–69 www.elsevier.com/locate/disc On some intriguing problems in …

The toughness of a (noncomplete) graph G is the minimum value of t for which there is a
vertex cut A whose removal yields components. Determining toughness is an NP‐hard …

We prove that for all an interval graph is‐Hamilton‐connected if and only if its scattering
number is at most k. This complements a previously known fact that an interval graph has a …

The toughness of a noncomplete graph G is the maximum real number t such that the ratio
of| S| to the number of components of G− S is at least t for every cutset S of G. Determining …

Abstract Chen et al.(1998) proved that every 18-tough chordal graph has a Hamilton cycle.
Improving upon their bound, we show that every 10-tough chordal graph is Hamiltonian (in …

A detour of a graph is a path of maximum length. A vertex that is common to all detours of a
graph is called a Gallai vertex. As a tool to prove the existence of a Gallai vertex, we …