Submission Type
Event
Expected Graduation Date
2016
Location
Room E102, Center for Natural Sciences, Illinois Wesleyan University
Start Date
4-18-2015 11:00 AM
End Date
5-18-2015 12:00 PM
Disciplines
Mathematics
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.
Included in
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.