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2000 | 20 | 1 | 93-103
Tytuł artykułu

Classes of hypergraphs with sum number one

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A hypergraph ℋ is a sum hypergraph iff there are a finite S ⊆ ℕ⁺ and d̲,d̅ ∈ ℕ⁺ with 1 < d̲ < d̅ such that ℋ is isomorphic to the hypergraph $ℋ_{d̲,d̅}(S) = (V,𝓔)$ where V = S and $𝓔 = {e ⊆ S: d̲ < |e| < d̅ ∧ ∑_{v∈ e} v∈ S}$. For an arbitrary hypergraph ℋ the sum number(ℋ ) is defined to be the minimum number of isolatedvertices $w₁,..., w_σ∉ V$ such that $ℋ ∪ {w₁,..., w_σ}$ is a sum hypergraph.
For graphs it is known that cycles Cₙ and wheels Wₙ have sum numbersgreater than one. Generalizing these graphs we prove for the hypergraphs 𝓒ₙ and 𝓦ₙ that under a certain condition for the edgecardinalities (𝓒ₙ)= (𝓦ₙ)=1
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
1
Strony
93-103
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-04
poprawiono
1999-09-28
Twórcy
  • Institute of Mathematics, Medical University of Lübeck, Wallstraße 40, 23560 Lübeck, Germany
Bibliografia
  • [1] C. Berge, Hypergraphs (North Holland, Amsterdam-New York-Oxford-Tokyo, 1989).
  • [2] D. Bergstrand, F. Harary, K. Hodges, G. Jennings, L. Kuklinski and J. Wiener, The Sum Number of a Complete Graph, Bull. Malaysian Math. Soc. (Second Series) 12 (1989) 25-28.
  • [3] M.N. Ellingham, Sum graphs from trees, Ars Combin. 35 (1993) 335-349.
  • [4] F. Harary, Sum Graphs and Difference Graphs, Congressus Numerantium 72 (1990) 101-108.
  • [5] F. Harary, Sum Graphs over all the integers, Discrete Math. 124 (1994)99-105, doi: 10.1016/0012-365X(92)00054-U.
  • [6] N. Hartsfield and W.F. Smyth, The Sum Number of Complete Bipartite Graphs, in: R. Rees, ed., Graphs and Matrices (Marcel Dekker, New York, 1992) 205-211.
  • [7] N. Hartsfield and W.F. Smyth, A family of sparse graphs with large sum number, Discrete Math. 141 (1995) 163-171, doi: 10.1016/0012-365X(93)E0196-B.
  • [8] M. Miller, Slamin, J. Ryan, W.F. Smyth, Labelling Wheels for Minimum Sum Number, J. Comb. Math. and Comb. Comput. 28 (1998) 289-297.
  • [9] M. Sonntag and H.-M. Teichert, Sum numbers of hypertrees, Discrete Math. 214 (2000) 285-290, doi: 10.1016/S0012-365X(99)00307-6.
  • [10] M. Sonntag and H.-M. Teichert, On the sum number and integral sum number of hypertrees and complete hypergraphs, Proc. 3rd Krakow Conf. on Graph Theory (1997), to appear.
  • [11] H.-M. Teichert, The sum number of d-partite complete hypergraphs, Discuss. Math. Graph Theory 19 (1999) 79-91, doi: 10.7151/dmgt.1087.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1109
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