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## Discussiones Mathematicae Graph Theory

2009 | 29 | 3 | 583-596
Tytuł artykułu

### Potentially H-bigraphic sequences

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We extend the notion of a potentially H-graphic sequence as follows. Let A and B be nonnegative integer sequences. The sequence pair S = (A,B) is said to be bigraphic if there is some bipartite graph G = (X ∪ Y,E) such that A and B are the degrees of the vertices in X and Y, respectively. If S is a bigraphic pair, let σ(S) denote the sum of the terms in A.
Given a bigraphic pair S, and a fixed bipartite graph H, we say that S is potentially H-bigraphic if there is some realization of S containing H as a subgraph. We define σ(H,m,n) to be the minimum integer k such that every bigraphic pair S = (A,B) with |A| = m, |B| = n and σ(S) ≥ k is potentially H-bigraphic. In this paper, we determine $σ(K_{s,t},m,n)$, σ(Pₜ,m,n) and $σ(C_{2t},m,n)$.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
583-596
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-06-05
zaakceptowano
2008-09-05
Twórcy
autor
• University of Colorado at Denver
autor
• University of Colorado at Denver
autor
• Middlebury College
autor
• Kyungpook National University
Bibliografia
• [1] F. Chung and R. Graham, Erdös on Graphs (A K Peters Ltd, 1998).
• [2] P. Erdös, M.S. Jacobson and J. Lehel, Graphs Realizing the Same Degree Sequence and their Respective Clique Numbers, in: Graph Theory, Combinatorics and Applications, Vol. I, ed. Alavi, Chartrand, Oellerman and Schwenk (1991) 439-449.
• [3] D. Gale, A theorem on flows in networks, Pac. J. Math. 7 (1957) 1073-1082.
• [4] R.J. Gould, M.S. Jacobson and J. Lehel, Potentially G-graphic degree sequences, in: Combinatorics, Graph Theory, and Algorithms Vol. I, eds. Alavi, Lick and Schwenk (New York: Wiley & Sons, Inc., 1999) 387-400.
• [5] C. Lai, The smallest degree sum that yields potentially Cₖ-graphical sequence, J. Combin. Math. Combin. Computing 49 (2004) 57-64.
• [6] J. Li and Z. Song, The smallest degree sum that yields potentially Pₖ-graphical sequences, J. Graph Theory 29 (1998) 63-72, doi: 10.1002/(SICI)1097-0118(199810)29:2<63::AID-JGT2>3.0.CO;2-A
• [7] J. Li, Z. Song and R. Luo, The Erdös-Jacobson-Lehel conjecture on potentially Pₖ-graphic sequences is true, Science in China (A) 41 (1998) 510-520, doi: 10.1007/BF02879940.
• [8] J. Li and J. Yin, The smallest degree sum that yields potentially K_{r,r}-graphic sequences, Science in China (A) 45 (2002) 694-705.
• [9] J. Li and J. Yin, An extremal problem on potentially K_{r,s}-graphic sequences, Discrete Math. 260 (2003) 295-305, doi: 10.1016/S0012-365X(02)00765-3.
• [10] R. Luo, On potentially Cₖ-graphic sequences, Ars Combin. 64 (2002) 301-318.
• [11] H.J. Ryser, Combinatorial properties of matrices of zeros and ones, Canad. J. Math. 9 (1957) 371-377, doi: 10.4153/CJM-1957-044-3.
• [12] K. Zarankiewicz, Problem P 101, Colloq. Math. 2 (1951) 301.
Typ dokumentu
Bibliografia
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