Discrete Mathematics & Theoretical Computer Science |

- 1 Department of Mathematics [Zhangzhou]

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 σ (K_p,1,1, n) denote the smallest degree sum such that every n-term graphical sequence S with σ (S)≥ σ (K_p,1,1, n) is potentially K_p,1,1 graphical. In this paper, we prove that σ (K_p,1,1, n)≥ 2[((p+1)(n-1)+2)/2] for n ≥ p+2. We conjecture that equality holds for n ≥ 2p+4. We prove that this conjecture is true for p = 3. AMS Subject Classifications: 05C07, 05C35

Source: HAL:hal-00959032v1

Volume: Vol. 7

Published on: January 1, 2005

Imported on: March 26, 2015

Keywords: 1-graphic,graph,degree sequence,potentially K_p,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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