Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge Weights
نویسنده
چکیده
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 are tight, since there exists a family of infinite bipartite graphs which are 2-connected and do not admit vertex-coloring S-edge-weightings for S ∈ {{0, 1}, {1, 2}}.
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ورودعنوان ژورنال:
- Discrete Mathematics & Theoretical Computer Science
دوره 17 شماره
صفحات -
تاریخ انتشار 2016