1 research outputs found
The maximum number of perfect matchings of semi-regular graphs
Let be an even integer, and . In this
paper, we prove that every -graph of order contains
disjoint perfect matchings. This result is sharp in the
sense that (i) there exists a -graph containing exactly
disjoint perfect matchings, and that (ii) there exists a
-graph without perfect matchings for each . As a
consequence, for any integer , every -graph of order
contains disjoint perfect matchings. This extends Csaba
et~al.'s breathe-taking result that every -regular graph of sufficiently
large order is -factorizable, generalizes Zhang and Zhu's result that every
-regular graph of order contains disjoint perfect
matchings, and improves Hou's result that for all , every
-graph of order contains
disjoint perfect matchings.Comment: 30 pages, 9 figure