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- W3156876633 abstract "The concept of rainbow disconnection number of graphs was introduced by Chartrand et al. (2018). Inspired by this concept, we put forward the concepts of rainbow vertex-disconnection and proper disconnection in graphs. In this paper, we first show that it is NP-complete to decide whether a given edge-colored graph G has a proper edge-cut separating two specified vertices, even though the graph G has $$Delta (G)=4$$ or is bipartite. Then, for a graph G with $$Delta (G)le 3$$ we show that $$pd(G)le 2$$ and distinguish the graphs with $$pd(G)=1$$ and 2, respectively. We also show that it is NP-complete to decide whether a given vertex-colored graph G is rainbow vertex-disconnected, even though the graph G has $$Delta (G)=3$$ or is bipartite." @default.
- W3156876633 created "2021-04-26" @default.
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- W3156876633 date "2021-04-16" @default.
- W3156876633 modified "2023-09-27" @default.
- W3156876633 title "Complexity results for two kinds of colored disconnections of graphs" @default.
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- W3156876633 doi "https://doi.org/10.1007/s10878-021-00742-0" @default.
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