Simple Proofs of Results on Paths Representing All Colors in Proper Vertex-Colorings

摘要

In this note we give simple proofs of two results which concerns paths representing all colors in optimal proper vertex-colorings of graphs. One result, due to Fung [2], is about the existence of colorful paths. The other one, due to Li [4], is about the existence of paths starting at any given vertex and representing all colors. Besides, we propose some open problems.