Complexity of graph covering problems
Given a fixed graph H, the H-cover problem asks whether an input graph G allows a degree preserving mapping f∶V(G)→V(H) such that for every v∈V(G), f(N G (v))=N H (f(v)). In this paper, we design efficient algorithms for certain graph covering problems according to two basic techniques. The first one is a reduction to the 2-SAT problem. The second technique exploits necessary and sufficient conditions for the existence of regular factors in graphs. For other infinite classes of graph covering problems we derive NP-completeness results by reductions from graph coloring problems. We illustrate this methodology by classifying all graph covering problems defined by simple graphs with at most 6 vertices.
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