Maxmaxflow and counting subgraphs

Bill Jackson, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We introduce a new graph invariant Λ(G) that we call maxmaxflow, and put it in the context of some other well-known graph invariants, notably maximum degree and its relatives. We prove the equivalence of two "dual" definitions of maxmaxflow: one in terms of flows, the other in terms of cocycle bases. We then show how to bound the total number (or more generally, total weight) of various classes of subgraphs of G in terms of either maximum degree or maxmaxflow. Our results are motivated by a conjecture that the modulus of the roots of the chromatic polynomial of G can be bounded above by a function of Λ(G).

    Original languageEnglish (US)
    Pages (from-to)1-46
    Number of pages46
    JournalElectronic Journal of Combinatorics
    Volume17
    Issue number1
    StatePublished - 2010

    Fingerprint

    Graph Invariants
    Maximum Degree
    Subgraph
    Counting
    Polynomials
    Chromatic Polynomial
    Cocycle
    Modulus
    Equivalence
    Roots
    Class
    Context

    Keywords

    • Chromatic polynomial
    • Cocycle
    • Degeneracy number
    • Flow
    • Graph
    • Maximum degree
    • Maxmaxflow
    • Second-largest degree
    • Subgraph

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Geometry and Topology
    • Theoretical Computer Science

    Cite this

    Jackson, B., & Sokal, A. D. (2010). Maxmaxflow and counting subgraphs. Electronic Journal of Combinatorics, 17(1), 1-46.

    Maxmaxflow and counting subgraphs. / Jackson, Bill; Sokal, Alan D.

    In: Electronic Journal of Combinatorics, Vol. 17, No. 1, 2010, p. 1-46.

    Research output: Contribution to journalArticle

    Jackson, B & Sokal, AD 2010, 'Maxmaxflow and counting subgraphs', Electronic Journal of Combinatorics, vol. 17, no. 1, pp. 1-46.
    Jackson, Bill ; Sokal, Alan D. / Maxmaxflow and counting subgraphs. In: Electronic Journal of Combinatorics. 2010 ; Vol. 17, No. 1. pp. 1-46.
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