## 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 C_{6} denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on *n* vertices** **into copies of C_{6} 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 C_{6} denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on *n* vertices** **into copies of C_{6} 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.