A sequence of the form s1s2 . . . sms1s2 . . . sm is called a repetition. A vertex-coloring of a graph is called nonrepetitive if none of its paths is repetitively colored. We ans...
Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-fa...
Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, She...
We proved that every planar triangle-free graph with n vertices has a subset of vertices that induces a forest of size at least (71n + 72)/128. This improves the earlier work of S...
Abstract. The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppste...
Recent work has shown that the physical connectivity of the Internet exhibits small-world behavior. Characterizing such behavior is important not only for generating realistic Int...