A note on orientation and chromatic number of graphs

A note on orientation and chromatic number of graphs

0.00 Avg rating0 Votes
Article ID: iaor20172788
Volume: 34
Issue: 2
Start Page Number: 605
End Page Number: 611
Publication Date: Aug 2017
Journal: Journal of Combinatorial Optimization
Authors:
Keywords: combinatorial optimization, graphs, heuristics
Abstract:

Let D be any edge orientation of a graph G. We denote by Δ k ( D ) equ1 the maximum value t for which there exists a directed path v 1 , , v k equ2 such that d o u t ( v k ) = t equ3 , where d o u t ( v k ) equ4 is the out‐degree of v k equ5 in D. We first obtain some bounds for the chromatic number of G in terms of Δ k ( D ) equ6 and then show a relationship between Δ k ( D ) equ7 and vertex partitions of a graph into degenerate subgraphs.

Reviews

Required fields are marked *. Your email address will not be published.