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Hamilton paths and 2-factors in self-complementary graphs
Abstract
A self complementary (SC) graph is a graph that is isomorphic to its complement. Clapham showed that every SC graph has a Hamilton path. We give an algorithm for constructing such a path given the complementing permutation π. Further, we give a new lower bound for the number of such paths in a SC graph G, answering a conjecture of Koh, Rao, and Vijayan. We continue by recharacterizing SC graphs which contain a 2-factor. (Rao gave the first such characterization.) We conclude by giving an algorithm that determines the existence of a 2-factor in a SC graph G having complementing permutation π. If G has a 2-factor, the algorithm continues on to construct a 2-factor.
Subject Area
Mathematics
Recommended Citation
Pollis, Timothy Kerwin, "Hamilton paths and 2-factors in self-complementary graphs" (1999). ETD collection for University of Nebraska-Lincoln. AAI9942146.
https://digitalcommons.unl.edu/dissertations/AAI9942146