Closure Concept Based on Degree-Sums of Independent Triples

摘要

The closure concept of Bondy and Chvatal is reviewed. The concept is based ondegree sums of pairs of nonadjacent vertices. A more general concept introduced by Ainouch and Christofides is shown to be able to be restated in terms of degree sums of independent triples. The concept is generalized. Simple graphs which have a Hamilton cycle are analyzed using the concept. The theories and proofs involved in the concept are outlined.