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The computational complexity of weighted vertex coloring for $$\{P_5,K_{2,3},K^+_{2,3}\}$${P5,K2,3,K2,3+} -free graphs
Optimization Letters ( IF 1.502 ) Pub Date : 2020-05-23 , DOI: 10.1007/s11590-020-01593-0
D. S. Malyshev, O. O. Razvenskaya, P. M. Pardalos

In this paper, we show that the weighted vertex coloring problem can be solved in polynomial on the sum of vertex weights time for \(\{P_5,K_{2,3}, K^+_{2,3}\}\)-free graphs. As a corollary, this fact implies polynomial-time solvability of the unweighted vertex coloring problem for \(\{P_5,K_{2,3},K^+_{2,3}\}\)-free graphs. As usual, \(P_5\) and \(K_{2,3}\) stands, respectively, for the simple path on 5 vertices and for the biclique with the parts of 2 and 3 vertices, \(K^+_{2,3}\) denotes the graph, obtained from a \(K_{2,3}\) by joining its degree 3 vertices with an edge.
更新日期:2020-05-23

 

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