Linear Hypergraph List Edge Coloring - Generalizations of the EFL Conjecture to List Coloring

Motivated by the Erdős-Faber-Lovász (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We discuss several conjectures for list edge coloring linear hypergraphs that generalize both EFL and Vizing's theorem for graphs. For example, we conjecture that in a...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-01
Main Author: Faber, Vance
Format: Article
Language:English
Subjects:
Graph coloring
Graph theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Motivated by the Erdős-Faber-Lovász (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We discuss several conjectures for list edge coloring linear hypergraphs that generalize both EFL and Vizing's theorem for graphs. For example, we conjecture that in a linear hypergraph of rank 3, the list edge chromatic number is at most 2 times the maximum degree plus 1. We show that for sufficiently large fixed rank and sufficiently large degree, the conjectures are true.
ISSN:2331-8422