Degree-doubling graph families

TL;DR

This paper investigates the maximum size of a family of degree-2 graphs on n vertices where the union of any two graphs results in a degree-4 graph, providing asymptotic bounds and discussing related problems.

Contribution

It determines the leading asymptotic term for the largest such graph family and explores similar problems in the domain.

Findings

Asymptotic formula for the maximum size of the family

Characterization of degree-doubling graph families

Discussion of related combinatorial problems

Abstract

Let G be a family of n-vertex graphs of uniform degree 2 with the property that the union of any two member graphs has degree four. We determine the leading term in the asymptotics of the largest cardinality of such a family. Several analogous problems are discussed.