科研之友
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摘要
For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e is not an element of G, there is a copy of F in G+Fe. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n, F). A graph G is weakly F-saturated if G contains no copy of F and there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs of order n that are weakly F-saturated will be denoted by wSAT(n, F), and those graphs in wSAT(n, F) with wsat(n, F) edges will be denoted by wSAT(n, F). The precise value of wsat(n, F) for many families of vertex disjoint copies of connected graphs such as small order graphs, trees, cycles, and complete graphs will be determined.
- 出版日期2014-12-6
