| Given a simple graph G,let V(G)={v1,v2,…,vn} be the vertex set of G, and let di be the degree of vi,i=1,2,…,n.Thenπis called the graphic sequence ifπis the degree sequence of a simple graph G and G is called a realization ofπ.For given a graph H,a graphic sequenceπ=(d1,d2,…,dn) is said to be potentially Hgraphic if there exists a realization ofπcontaining H as a subgraph.Let Kr+1-H( H is a subgraph of Kr+1) denote a graph obtained from Kr+1 by removing the edges sets E(H).This thesis mainly consider the criterions on potentially K6-H graphic sequences in degree sequences.The following results are obtained in this thesis:1,We give a necessary and sufficient condition for a sequence to be potentially H-graphic,we also give a necessary and sufficient condition for a sequence to be graphic if the maximal degree is at most 5.2,We characterize the potentially K6-C5-graphic sequences.3,We characterize the potentially K6-(K2,3-e)-graphic sequences. |
