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On the Chromatic Edge Stability Number of Graphs

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Abstract

The chromatic edge stability number \( es _{\chi }(G)\) of a graph G is the minimum number of edges whose removal results in a graph \(H \subseteq G\) with chromatic number \(\chi (H) = \chi (G) - 1\). The chromatic bondage number \(\rho (G)\) of G is the minimum number of edges between any two color classes in a \(\chi (G)\)-coloring of G, where the minimum is taken over all \(\chi (G)\)-colorings of G. In this paper, we characterize graphs for which these two parameters coincide. Moreover, we give general bounds and we determine these parameters for several classes of graphs.

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Authors and Affiliations

  1. Computational Mathematics, TU Braunschweig, Braunschweig, Germany

    Arnfried Kemnitz & Massimiliano Marangio

  2. IRC, Kalasalingam University, Krishnan Kovil, Tamil Nadu, India

    Nazanin Movarraei

Authors
  1. Arnfried Kemnitz
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  2. Massimiliano Marangio
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  3. Nazanin Movarraei
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Correspondence to Arnfried Kemnitz.

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Kemnitz, A., Marangio, M. & Movarraei, N. On the Chromatic Edge Stability Number of Graphs. Graphs and Combinatorics 34, 1539–1551 (2018). https://doi.org/10.1007/s00373-018-1972-y

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  • DOI: https://doi.org/10.1007/s00373-018-1972-y

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