%0 Journal Article
%T An extremal problem on potentially K p,1,1-graphic sequences
%A Chunhui Lai
%J Discrete Mathematics & Theoretical Computer Science
%D 2005
%I Discrete Mathematics & Theoretical Computer Science
%X A sequence S is potentially K p,1,1 graphical if it has a realization containing a K p,1,1 as a subgraph, where K p,1,1 is a complete 3-partite graph with partition sizes p,1,1. Let ¦Ò(K p,1,1, n) denote the smallest degree sum such that every n-term graphical sequence S with ¦Ò(S)¡Ý ¦Ò(K p,1,1, n) is potentially K p,1,1 graphical. In this paper, we prove that ¦Ò (K p,1,1, n)¡Ý 2[((p+1)(n-1)+2)/2] for n ¡Ý p+2. We conjecture that equality holds for n ¡Ý 2p+4. We prove that this conjecture is true for p = 3. AMS Subject Classifications: 05C07, 05C35
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/63