2015•Digital Commons at Illinois Wesleyan University (Illinois Wesleyan University)Open access
Multidecompositions of Complete Graphs into a Graph Pair of Order 6
Yizhe Gao, Faculty Advisor Roberts
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Abstract
A graph is a mathematical structure consisting of a set of objects called vertices and a set of 2-element subsets of vertices, called edges. The complete graph on n vertices is the graph with n vertices and an edge between any pair of distinct vertices. Let C6 denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on n vertices into copies of C6 and its complement with at least one copy of each graph. We provide necessary and sufficient conditions on n for the existence such a structure.
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