Year: 2026
Type: preprint
Abstract: We study the common spanning structure of connected finite simple graphs that are indistinguishable by uniformly initialized color refinement. We prove that any two such graphs with common cyclomatic number $r\ge2$ contain isomorphic spanning forests with at most $r-1$ components. This bound depends only on $r$ and is sharp for every $r\ge2$, even when both graphs have maximum degree at most three. We also determine the maximum, over all such graph pairs without restricting their order, of the minimum edge symmetric difference under vertex bijections: it is exactly $4(r-1)$.
Source: arXiv (Cornell University)
Author: Zhu, Jianshen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222966168