Research On Randomly Decomposing And Packing Problems Of Graphs

The randomly packing and decomposing problems of simple graphs are active re-search problems in Graph Theory. A graph G is called randomly H decomposable ifevery maximal H packing in G uses all edges of G. G is called H equipackable if everymaximal H packing in G is also maximum in G. Randomly M2decomposable graphs,randomly M3decomposable graphs, M2equipackable graphs, M2decomposable multi-graphs and M3decomposable multigraphs have been characterized. In this paper, wefirstly research on randomly Mt decomposable graphs, and get some notes. Then, allrandomly M2decomposable multigraphs, randomly M3decomposable multigraphs,and some basic theories about randomly Mt decomposable multigraphs are character-ized. Finally, all M2equipackable multigraphs are characterized.