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发表于 2025-3-25 05:29:24 | 显示全部楼层
https://doi.org/10.1007/978-3-658-15658-9 For . = 1, this gives the usual notion of matching in graphs, and for general . ≥ 1, distance-. matchings were called . by Stockmeyer and Vazirani. The special case . = 2 has been studied under the names . (i.e., a matching which forms an induced subgraph in .) by Cameron and . by Golumbic and Lask
发表于 2025-3-25 10:46:03 | 显示全部楼层
https://doi.org/10.1007/978-3-662-69201-1write . ∈ Ψ(.), if . is a maximum stable set of the subgraph induced by . ∪ .(.), where .(.) is the neighborhood of .,[11]. Nemhauser and Trotter Jr. proved that any . ∈ Ψ(.) is a subset of a maximum stable set of .,[19]..In this paper we demonstrate that if . ∈ Ψ(.), the subgraph . induced by . ∪ .
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https://doi.org/10.1007/978-3-658-01900-6status of the problem is not known if the input is restricted to graphs with no cycles of length 4. We conjecture that the problem is polynomial if the input graph does not contain cycles of length 4 and 6, and prove several theorems supporting our conjecture.
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https://doi.org/10.1007/978-3-658-40421-5w some known results and prove new ones. In particular, we consider a family of transformations of an edge-coloured multigraph . into an ordinary graph that allow us to check the existence of PC cycles and PC (.,.)-paths in . and, if they exist, to find shortest ones among them. We raise a problem o
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