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Random subgraphs of regular graphs

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  • First Online:
Graph Theory Singapore 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1073))

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Abstract

Let G denote a connected r-regular labelled graph. Denote by RG(p) any subgraph of G having the same point set as G and line set defined by selecting or rejecting each of the lines of G with independent probability p or q=1−p, respectively. Since RG(p) is the outcome of a random process, RG(p) is called a random subgraph of G and is studied with the appropriate probabilistic considerations.

We derive some general properties of RG(p). In particular, we obtain the generating function for the point degree distribution of RGj(p), the subgraph of RG(p) induced by the points of RG(p) having degree greater than or equal to j. We also comment on a possible relation between pc, the critical probability for the existence of an infinite order component in RG(p), and p cr , the analogous critical probability for RGr (p).

This work was supported by grants from Research Corporation, the Pace University Scholarly Research Committee, and the Kenan Fund.

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Authors and Affiliations

  1. Mathematics Department, Pace University, 10038, New York, NY, U.S.A.

    Louis V. Quintas

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  1. Louis V. Quintas
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Khee Meng Koh Hian Poh Yap

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© 1984 Springer-Verlag

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Quintas, L.V. (1984). Random subgraphs of regular graphs. In: Koh, K.M., Yap, H.P. (eds) Graph Theory Singapore 1983. Lecture Notes in Mathematics, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073113

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  • DOI: https://doi.org/10.1007/BFb0073113

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13368-1

  • Online ISBN: 978-3-540-38924-8

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