Elementary graphs with respect to (1, f)-odd factors
نویسندگان
چکیده
This note concerns the (1, f)-odd subgraph problem, i.e. we are given an undirected graph G and an odd value function f : V (G) → N, and our goal is to find a spanning subgraph F of G with degF ≤ f minimizing the number of even degree vertices. First we prove a Gallai–Edmonds type structure theorem and some other known results on the (1, f)-odd subgraph problem, using an easy reduction to the matching problem. Then we use this reduction to investigate barriers and elementary graphs with respect to (1, f)odd factors, i.e. graphs where the union of (1, f)-odd factors form a connected spanning subgraph.
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