Friday, November 22 2019

12:30pm - 2:00pm

12:30pm - 2:00pm

Masters Presentation

Eric Culver MS Applied Math Project

Title: Applying the Potential Method to the Edge List Coloring Conjecture

Abstract: We report on recent results on the Edge List Coloring Conjecture, including new results discovered by the author. The Edge List Coloring Conjecture states that for a graph G the edge chromatic number is equal to the edge list chromatic number (as known as edge choosability). If proved, this would be a surprising result since the vertex list chromatic number can be arbitrarily large compared to the vertex chromatic number. Woodall showed that any graph with mad(G) < sqrt(2*Delta(G)) satisfies the conjecture using iterated discharging. This maximum average degree bound is equivalent to saying that a certain potential of G is nonnegative. We will use the iterated discharging method of Woodall combined with the potential method to extend his result to graphs with potential above a negative bound.

Abstract: We report on recent results on the Edge List Coloring Conjecture, including new results discovered by the author. The Edge List Coloring Conjecture states that for a graph G the edge chromatic number is equal to the edge list chromatic number (as known as edge choosability). If proved, this would be a surprising result since the vertex list chromatic number can be arbitrarily large compared to the vertex chromatic number. Woodall showed that any graph with mad(G) < sqrt(2*Delta(G)) satisfies the conjecture using iterated discharging. This maximum average degree bound is equivalent to saying that a certain potential of G is nonnegative. We will use the iterated discharging method of Woodall combined with the potential method to extend his result to graphs with potential above a negative bound.

Speaker: | Eric Culver |

Affiliation: | |

Location: | 4017 |

Done