Supereulerian regular matroids without small cocircuits

Abstract

AbstractA cycle of a matroid is a disjoint union of circuits. A matroid is supereulerian if it contains a spanning cycle. To answer an open problem of Bauer in 1985, Catlin proved in [J. Graph Theory 12 (1988) 29–44] that for sufficiently large , every 2‐edge‐connected simple graph with and minimum degree is supereulerian. In [Eur. J. Combinatorics, 33 (2012), 1765–1776], it is shown that for any connected simple regular matroid , if every cocircuit of satisfies , then is supereulerian. We prove the following. (i) Let be a connected simple regular matroid. If every cocircuit of satisfies , then is supereulerian. (ii) For any real number with , there exists an integer such that if every cocircuit of a connected simple cographic matroid satisfies , then is supereulerian.