| Summary: | 碩士 === 淡江大學 === 數學學系碩士班 === 98 === A complete graph with n vertices is a simple graph in which every pair of distinct vertices is connected by a unique edge, denoted by K_n.
The cycle is a connected graph with n vertices which all vertices are degree 2 and denoted by C_n.
A complete graph K_n can be decomposed into 4-cycles and n-cycles if K_n can be partitioned into edge-disjoint 4-cycles and n-cycles such that the union of edge sets of these cycles is the edge set of K_n.
In this thesis, we prove that:
(1) For odd integer n, n≥3, if there exists nonnegative integers α and β such that 4α+βn=(n(n-1))/2 , then K_n can be decomposed into α 4-cycles and β n-cycles.
(2) For even integer n, n≥4, if there exists nonnegative integers α and β such that 4α+βn=(n(n-2))/2 , then K_n-I can be decomposed into α
4-cycles and β n-cycles, where I is a 1-factor of K_n.
|
|---|
