The circumference conjecture for connected matroid pathwidth

Let MM be a connected matroid with rank function rr. Its circumference is the maximum size of a circuit of MM, when MM has at least one circuit, and its pathwidth is denoted by pw(M)\operatorname{pw}(M). Connected matroid circumference conjecture. Every connected matroid MM with circumference kk has pathwidth O(k)O(k). This conjecture seeks a linear upper bound on the pathwidth of connected matroids in terms of their circumference, generalizing analogous bounds for 22-connected graphs. The source does not state whether the conjecture is known or resolved.

Sources & referencesView supporting material

Primary source

Marcin Briański, Gwenaël Joret and Michał T. Seweryn, “Pathwidth vs cocircumference”, arXiv:2306.03621 (2023).

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