Edge Coloring Bipartite Graphs Eeciently

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...