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Existence of subgraph with orthogonal (g,f)-factorization

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Abstract

Simple graphs are considered. Let G be a graph andg(x) andf(x) integer-valued functions defined on V(G) withg(x)⩽f(x) for everyxɛV(G). For a subgraphH ofG and a factorizationF=|F 1,F 2,⃛,F 1| ofG, if |E(H)∩E(F 1)|=1,1⩽i⩽j, then we say thatF orthogonal toH. It is proved that for an (mg(x)+k,mf(x) -k)-graphG, there exists a subgraphR ofG such that for any subgraphH ofG with |E(H)|=k,R has a (g,f)-factorization orthogonal toH, where 1⩽k<m andg(x)⩾1 orf(x)⩾5 for everyxɛV(G).

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Authors and Affiliations

  1. Institute of Applied Mathematics, Chinese Academy of Sciences, 100080, Beijing, China

    Yan Guiying

  2. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China

    Pan Jiaofeng

Authors
  1. Yan Guiying
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  2. Pan Jiaofeng
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Project supported by the Chitia Postdoctoral Science Foundation and Chuang Xin Foundation of the Chinese Academy of Sciences.

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Guiying, Y., Jiaofeng, P. Existence of subgraph with orthogonal (g,f)-factorization. Sci. China Ser. A-Math. 41, 48–54 (1998). https://doi.org/10.1007/BF02900771

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  • DOI: https://doi.org/10.1007/BF02900771

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