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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Phuong-Lan Nguyen
UCO, Angers, France
Electrical & Electronics Engineering

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Graphs with coloring redundant edges Bart Demoen; Phuong-Lan Nguyen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.2.9

Abstract

A graph edge is $d$-coloring redundant if the removal of the edge doesnot change the set of $d$-colorings of the graph. Graphs that are toosparse or too dense do not have coloring redundant edges. Tight upperand lower bounds on the number of edges in a graph in order for thegraph to have a coloring redundant edge are proven. Two constructionslink the class of graphs with a coloring redundant edge to the$K_4$-free graphs and to the uniquely colorable graphs. The structureof graphs with a coloring redundant edge is explored.
Co-Authors Bart Demoen