Anti-Path Cover on Sparse Graph Classes
نویسندگان
چکیده
Graph Hamiltonian properties are studied especially in connection with graph connectivity properties. A graph is called Hamiltonian if there is a path passing through all its vertices in that graph. In this work we are interested in sparse graph setting for which this question was already solved e.g. using the famous theorem of Courcelle [4]. It is possible to express the Hamiltonian property by an MSO2 formula and thus resolve the question by an FPT algorithm. For a graph G and a positive integer k we say that G is k-path coverable if there exists a collection of at most k vertex disjoint paths in G such that the vertices of G are the union of vertices of all paths in the collection (that is, each vertex belongs to exactly one path in the collection). We give a simple, but interesting, twist to the question to rise a new problem:
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