#### Title of Presentation

Multidecompositions of Complete Graphs into a Graph Pair of Order 6

#### Type of Submission

Event

#### 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

#### 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.