Edge growth in graph squares

Details Edge growth in graph squares Edge growth in graph squares

2011-12-21

arxiv.org/abs/1112.5157v1

Mathematics

Combinatorics

Scientific paper

We resolve a conjecture of Hegarty regarding the number of edges in the
square of a regular graph. If $G$ is a connected $d$-regular graph with $n$
vertices, the graph square of $G$ is not complete, and $G$ is not a member of
two narrow families of graphs, then the square of $G$ has at least
$(2-o_d(1))n$ more edges than $G$.

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