Edge-Coloring Bipartite Graphs

Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge Weights

It was proved that every 3-connected bipartite graph admits a vertex-coloring S-edge-weighting for S = {1, 2} (H. Lu, Q. Yu and C. Zhang, Vertex-coloring 2-edge-weighting of graphs, European J. Combin., 32 (2011), 22-27). In this paper, we show that every 2-connected and 3-edge-connected bipartite graph admits a vertex-coloring S-edgeweighting for S ∈ {{0, 1}, {1, 2}}. These bounds we obtain ar...

Interval non-edge-colorable bipartite graphs and multigraphs

An edge-coloring of a graph G with colors 1, . . . , t is called an interval t-coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In 1991 Erdős constructed a bipartite graph with 27 vertices and maximum degree 13 which has no interval coloring. Erdős’s counterexample is the smallest (in a sense of maximum degree) k...

On interval edge-colorings of bipartite graphs of small order

An edge-coloring of a graph G with colors 1, . . . , t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. The problem of deciding whether a bipartite graph is interval colorable is NP-complete. The smalle...

Finding 1-Factors in Bipartite Regular Graphs and Edge-Coloring Bipartite Graphs

Another Simple Algorithm for Edge-Coloring Bipartite Graphs

A new edge-coloring algorithm for bipartite graphs is presented. This algorithm, based on the framework of the O(m log d + (m/d) log(m/d) log d) algorithm by Makino–Takabatake–Fujishige and the O(m log m) one by Alon, finds an optimal edge-coloring of a bipartite graph with m edges and maximum degree d in O(m log d + (m/d) log(m/d)) time. This algorithm does not require elaborate data structure...

On the simultaneous edge coloring of graphs

A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et a...