Graduation Year

2016

Location

Room E102, Center for Natural Sciences, Illinois Wesleyan University

Start Date

18-4-2015 11:00 AM

End Date

18-5-2015 12:00 PM

Description

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.

Included in

Mathematics Commons

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Apr 18th, 11:00 AM May 18th, 12:00 PM

Multidecompositions of Complete Graphs into a Graph Pair of Order 6

Room E102, Center for Natural Sciences, Illinois Wesleyan University

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.