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- W4200203203 abstract "Since many NP-complete graph problems have been shown polynomial-time solvable when restricted to claw-free graphs, we study the problem of determining the distance of a given graph to a claw-free graph, considering vertex elimination as measure. CLAW-FREE VERTEX DELETION (CFVD) consists of determining the minimum number of vertices to be removed from a graph such that the resulting graph is claw-free. Although CFVD is NP-complete in general and recognizing claw-free graphs is still a challenge, where the current best algorithm for a graph $G$ has the same running time of the best algorithm for matrix multiplication, we present linear-time algorithms for CFVD on weighted block graphs and weighted graphs with bounded treewidth. Furthermore, we show that this problem can be solved in linear time by a simpler algorithm on forests, and we determine the exact values for full $k$-ary trees. On the other hand, we show that CLAW-FREE VERTEX DELETION is NP-complete even when the input graph is a split graph. We also show that the problem is hard to approximate within any constant factor better than $2$, assuming the Unique Games Conjecture." @default.
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- W4200203203 date "2021-12-14" @default.
- W4200203203 modified "2023-10-08" @default.
- W4200203203 title "Linear‐time algorithms for eliminating claws in graphs" @default.
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- W4200203203 doi "https://doi.org/10.1111/itor.13100" @default.
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