Geodesic
An extremal problem on potentially K_p,1,1-graphic sequences
Discrete mathematics & theoretical computer science, Tome 7 (2005).

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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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     author = {Lai, Chunhui},
     title = {An extremal problem on potentially {K_p,1,1-graphic} sequences},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2005},
     doi = {10.46298/dmtcs.357},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.357/}
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Lai, Chunhui. An extremal problem on potentially K_p,1,1-graphic sequences. Discrete mathematics & theoretical computer science, Tome 7 (2005). doi : 10.46298/dmtcs.357. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.357/

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