蕴含K_5-Z_5可图序列的刻划

On Potentially K_(1,4)+e -Graphic Sequences

对于给定的图H,称π是蕴含H可图的,如果π有一个实现包含H作为子图.K k,C k,Pk分别表示k阶完全图,圈长为k的圈和路长为k的路.Z 5是由一个公共顶点的C3和P2组成的图,K 5-Z5表示从5阶完全图中删去Z 5的5条边.Luo Rong[13]考虑了蕴含C k可图序列的刻划问题,并刻划了当k=3,4,5时,蕴含C k的可图序列.此外,Luo等人[14]刻划了蕴含K 4的可图序列.Eschen和Niu[15]刻划了蕴含K 4-e的可图序列.Yin Jianhua等人[20]刻划了当r=2,s=3和r=2,s=4时,蕴含K r,s的可图序列,其中K r,s是r×s完全二部图.Hu Lili等人[3-5]刻划了蕴含K 5-C4,K 5-Z4,K 5-E3的可图序列,徐正华等人[16]刻划了K1,4+e的可图序列.本文刻划了当n≥5时,蕴含K 5-Z5的可图序列.

For Given a graph H , a graphic sequence π = （d1,d2,…,dn ） is said to be potentially H graphical if it has a realization containing H as a subgraph. Let Kk , Ck and Pk denote a complete graph on k vertices, a cycle on k vertices and a path on k ＋ 1 vertices, respectively. Let Z5 be a graph obtained by add P2 to C3 and they have a same vertices. Let K5 -Z5 be a graph obtained by delete Z5 to K5 which has 5 vertices and 5 edges. Luo Rong^[13] characterized the potentially Ck -graphic sequences for each k = 3,4,5. Recently, Luo and Warner^[14] characterized the potentially K4 -graphic sequences. Eschen and Niu^[15] characterized the potentially K4 - e- graphic sequences . Yin and Chen^[12] characterized the potentially Kr.s -graphic sequences for r = 2,s = 3 and r = 2, S = 4. Hu and Lai^[3-5] characterize the potentially K 5-C4, K5-Z4 and K5 - E3 -graphic sequences. Xu and Hu^[16] characterize the potentially K1,4 ＋ e -graphic sequences. In this paper, we characterize the potentially K5 - Z5 -graphic sequences.