Graphs with the same truncated cycle matroid

Published 30 Sep 2022 in math.CO and cs.DM | (2209.15183v1)

Abstract: The classical Whitney's 2-Isomorphism Theorem describes the families of graphs having the same cycle matroid. In this paper we describe the families of graphs having the same truncated cycle matroid and prove, in particular, that every 3-connected graph, except for K4, is uniquely defined by its truncated cycle matroid.

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