# On cyclic decompositions of Kn-1,n-1 +I into a 2-regular bipartite graph with at most 2 components

## Document Type

Oral Presentation

SURC Room 202

15-5-2014

15-5-2014

## Keywords

Cyclic graph decompositions, 2-Regular graphs, I-factor

## Abstract

Here, I represents a factor added to an already complete bipartite graph (Kn-1, n-1). A bigraph is way to represent relationships between two independent sets of objects called vertices. Each vertex of one set connects to one or more vertices in the other set by what is called an edge. For example, the two sets could be NFL football conferences, the vertices are the various teams, and the edges connect teams of the two conferences that have played each other. To carry this example further, edges connect the Seattle Seahawks (vertex) of the NFC West (set) to the Washington Redskins, Dallas Cowboys, and New York Giants, the NFC East teams the Seahawks played in 2011. Cycles are sequences of vertices. Cyclic decomposition is the partitioning of the vertices into subsets based on edge patterns. In complete bigraphs, every vertex of one set is connected to every vertex of the second set. In a regular graph, each vertex has the same number of neighbors. In summer 2013, I participated in a Research Experience for Undergraduates at Illinois State University with Professor Saad El-Zanati, who investigates combinatorics and graph theory. Professor El-Zanati asked our team to expand the previous results by adding another factor in Kn−1,n−1 + I, to the complete bigraphs. We found patterns based on vertex labelings of G that allowed us to obtain cyclic G-decompositions of Kn-1,n-1+I.

## Faculty Mentor(s)

Buvit, Ian

McNair Scholars Program

## Share

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May 15th, 10:00 AM May 15th, 10:20 AM

On cyclic decompositions of Kn-1,n-1 +I into a 2-regular bipartite graph with at most 2 components

SURC Room 202

Here, I represents a factor added to an already complete bipartite graph (Kn-1, n-1). A bigraph is way to represent relationships between two independent sets of objects called vertices. Each vertex of one set connects to one or more vertices in the other set by what is called an edge. For example, the two sets could be NFL football conferences, the vertices are the various teams, and the edges connect teams of the two conferences that have played each other. To carry this example further, edges connect the Seattle Seahawks (vertex) of the NFC West (set) to the Washington Redskins, Dallas Cowboys, and New York Giants, the NFC East teams the Seahawks played in 2011. Cycles are sequences of vertices. Cyclic decomposition is the partitioning of the vertices into subsets based on edge patterns. In complete bigraphs, every vertex of one set is connected to every vertex of the second set. In a regular graph, each vertex has the same number of neighbors. In summer 2013, I participated in a Research Experience for Undergraduates at Illinois State University with Professor Saad El-Zanati, who investigates combinatorics and graph theory. Professor El-Zanati asked our team to expand the previous results by adding another factor in Kn−1,n−1 + I, to the complete bigraphs. We found patterns based on vertex labelings of G that allowed us to obtain cyclic G-decompositions of Kn-1,n-1+I.