![]() ![]() Wang, Y., Wang, W., Wang, Y.: Edge-partition and star chromatic index. Lužar, B., Mockovčiaková, M., Soták, R.: Note on list star edge-coloring of subcubic graphs. S., Deng, K.: An upper bound on the star chromatic index of graphs with Δ ≥ 7. X.: Star chromatic index of subcubic multigraph. Kerdjoudj, S., Pradepp, K., Raspaud, A.: List star chromatic index of sparse graphs. Kerdjoudj, S., Raspaud, A.: List star edge coloring of sparse graphs. Kerdjoudj, S., Kostochka, A., Raspaud, A.: List star edge coloring of subcubic graphs. A short proof of a known upper bound for x (G), again in terms of vertex degrees, is also given. Han, M., Li, J., Luo, R., et al.: List star edge coloring of k-degenerate graphs. Grünbaum, B.: Acyclic colorings of planar graphs. We have shown that the upper bound is sharp for forests. What are the possible values of c g (G) for all graphs G Corollary 1 gives upper bounds on the circular game chromatic number of these classes of graphs. Graph Theory, 72, 313–326 (2013)įertin, G., Raspaud, A., Reed, B.: On star coloring of graphs, Lecture Notes 483 in Comput. Thus, it is not difficult to see that no graph has circular game chromatic number in the open interval (2, 4). There is some hope that higher levels of the. However, there exist graphs for which the Lovasz theta gives a lowerbound of k O ( 1) and the chromatic number is at least n 1 2 / k. Graph Theory, 81(1), 73–82 (2016)ĭeng, K., Liu, X., Tian, S.: Star edge coloring of trees (in Chinese.) J. In general, if you have an upper bound U on the integrality gap of the SDP, you can scale the objective of the SDP by U and youll get an upper bound as well. The proof applies a newly developed coloring extension method by assigning color sets with different sizes.īezegová, L., Lužar, B., Mockovčiaková, M., et al.: Star edge coloring of some classes of graphs. The star chromatic index \(\chi _\) of Δ is the best possible. A star k-edge-coloring is a proper k-edge-coloring such that every connected bicolored subgraph is a path of length at most 3. ![]()
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