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An extremal problem on potentially Kp,1,1-graphic sequences

Abstract : 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
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Chunhui Lai. An extremal problem on potentially Kp,1,1-graphic sequences. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2005, Vol. 7, pp.75-80. ⟨10.46298/dmtcs.357⟩. ⟨hal-00959032⟩



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