Author:

Keywords:

graph coloring, extremal problems, Science & Technology, Physical Sciences, Mathematics, coloring of graphs and hypergraphs, 4901 Applied mathematics

Abstract:

A graph edge is $d$-coloring redundant if the removal of the edge does not change the set of $d$-colorings of the graph. Graphs that are too sparse or too dense do not have coloring redundant edges. Tight upper and lower bounds on the number of edges in a graph in order for the graph to have a coloring redundant edge are proven. Two constructions link the class of graphs with a coloring redundant edge to the $K_4$-free graphs and to the uniquely colorable graphs. The structure of graphs with a coloring redundant edge is explored.