On the potentially Pk-graphic sequences

On the potentially Pk - graphic sequences 1 Jiong - Sheng

A nonincreasing sequence n of n nonnegative integers is said to be graphic if it is the degree sequence of a simple graph G of order n and G is called a realization of n. A graph G of order n is said to have property P, if it contains a clique of size k as a subgraph. An n-term graphic sequence n is said to be potentially (res. forcibly)Pk-graphic if it has a realization having (res. all its re...

On potentially (K4-e)-graphic sequences

In this paper, we characterize the potentially (K4 − e)-graphic sequences where K4 − e is the graph obtained from K4 by removing one edge. This characterization implies a theorem due to C. H. Lai (Australas. J. Combin. 24 (2001), 123–127) and a characterization of potentially C4graphic sequences due to R. Luo (Ars Combin. 64 (2002), 301–318).

On potentially P-graphic degree sequences

A sequence 1l = (d 1 ,d 2 , ... ,d n) of positive integers is said to be graphic if there exists a simple graph G such that 1£ is the degree sequence of G. For a specified property P of graphs. a sequence 1l = (d 1 ,d 2 • ... • d n) of positive integers is said to be potentially P-graphic if 1l is graphic and there exists a realization of 1l with the property P. In this paper we characterize po...

An Extremal Problem On Potentially Kr+1-H-graphic Sequences

A sequence S is potentially Kp,1,1 graphical if it has a realization containing a Kp,1,1 as a subgraph, where Kp,1,1 is a complete 3-partite graph with partition sizes p, 1, 1. Let σ(Kp,1,1, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Kp,1,1, n) is potentially Kp,1,1 graphical. In this paper, we prove that σ(Kp,1,1, n) ≥ 2[((p + 1)(n − 1) + 2)/2] ...

A note on potentially K1, 1, t-graphic sequences