Odd subgraphs and matchings |
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Authors: | M. Kano Gyula Y. Katona |
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Affiliation: | a Department of Computer and Information Sciences, Ibaraki University, Nakanarusawa, Hitachi, 316-8511 Japan b Department of Computer and Information Sciences, Budapest University of Technology and Economics, Budapest, Pob.: 91, 1521, Hungary |
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Abstract: | Let G be a graph and f : V(G)→{1,3,5,…}. Then a subgraph H of G is called a (1,f)-odd subgraph if degH(x){1,3,…,f(x)} for all xV(H). If f(x)=1 for all xV(G), then a (1,f)-odd subgraph is nothing but a matching. A (1,f)-odd subgraph H of G is said to be maximum if G has no (1,f)-odd subgraph K such that |K|>|H|. We show that (1,f)-odd subgraphs have some properties similar to those of matchings, in particular, we give a formula for the order of a maximum (1,f)-odd subgraph, which is similar to that for the order of a maximum matching. |
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Keywords: | Odd subgraph Graph factor Matching |
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