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The computational complexity of weighted vertex coloring for \(\{P_5,K_{2,3},K^+_{2,3}\}\)-free graphs

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Abstract

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.

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Acknowledgements

Research is supported under financial support of Russian Science Foundation, project No 19-71-00005.

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Authors and Affiliations

  1. National Research University Higher School of Economics, 25/12 Bolshaja Pecherskaja Ulitsa, Nizhny Novgorod, Russia, 603155

    D. S. Malyshev & O. O. Razvenskaya

  2. University of Florida, 401 Weil Hall, P.O. Box 116595, Gainesville, FL, 326116595, USA

    P. M. Pardalos

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  1. D. S. Malyshev
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  2. O. O. Razvenskaya
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  3. P. M. Pardalos
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Correspondence to D. S. Malyshev.

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Malyshev, D.S., Razvenskaya, O.O. & Pardalos, P.M. The computational complexity of weighted vertex coloring for \(\{P_5,K_{2,3},K^+_{2,3}\}\)-free graphs. Optim Lett 15, 137–152 (2021). https://doi.org/10.1007/s11590-020-01593-0

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