Biased graphs with no two vertex-disjoint unbalanced cycles

Rong Chen, Irene Pivotto

    Research output: Contribution to journalArticle

    Abstract

    Lovász has completely characterised the structure of graphs with no two vertex-disjoint cycles, while Slilaty has given a structural characterisation of graphs with no two vertex-disjoint odd cycles; his result is in fact more general, describing signed graphs with no two vertex-disjoint negative cycles. A biased graph is a graph with a distinguished set of cycles (called balanced) with the property that any theta subgraph does not contain exactly two balanced cycles. In this paper we characterise the structure of biased graphs with no two vertex-disjoint unbalanced cycles, answering a question by Zaslavsky and generalising the results of Lovász and Slilaty.

    Original languageEnglish
    Pages (from-to)207-245
    Number of pages39
    JournalJournal of Combinatorial Theory. Series B
    Volume130
    DOIs
    Publication statusPublished - 1 May 2018

      Fingerprint

    Cite this