The circumference conjecture for connected matroid pathwidth
The circumference conjecture for connected matroid pathwidth
Let be a connected matroid with rank function . Its circumference is the maximum size of a circuit of , when has at least one circuit, and its pathwidth is denoted by . Connected matroid circumference conjecture. Every connected matroid with circumference has pathwidth . This conjecture seeks a linear upper bound on the pathwidth of connected matroids in terms of their circumference, generalizing analogous bounds for -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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