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- W2765982665 abstract "The famous Kőnig‐Egervary theorem is equivalent to the statement that the matching number equals the vertex cover number for every induced subgraph of some graph if and only if that graph is bipartite. Inspired by this result, we consider the set Gk of all graphs such that, for every induced subgraph, the maximum number of disjoint paths of order k equals the minimum order of a set of vertices intersecting all paths of order k. For k ∈ {3,4}, we give complete structural descriptions of the graphs in Gk. Furthermore, for odd k, we give a complete structural description of the graphs in Gk that contain no cycle of order less than k. For these graph classes, our results yield efficient recognition algorithms as well as efficient algorithms that determine maximum sets of disjoint paths of order k and minimum sets of vertices intersecting all paths of order k." @default.
- W2765982665 created "2017-11-10" @default.
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- W2765982665 date "2017-10-24" @default.
- W2765982665 modified "2023-09-27" @default.
- W2765982665 title "On the Kőnig-Egerváry Theorem for $k$-Paths" @default.
- W2765982665 hasPublicationYear "2017" @default.
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