Yokoi's conjecture
András Biró (2003)
Acta Arithmetica
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András Biró (2003)
Acta Arithmetica
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G. Besson (2009)
Bollettino dell'Unione Matematica Italiana
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Fuzhen Zhang (2016)
Special Matrices
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We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We...
Paule, Peter (1996)
Experimental Mathematics
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K. Kubota (1977)
Acta Arithmetica
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K. Inkeri (1976)
Acta Arithmetica
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W. Narkiewicz (1977)
Colloquium Mathematicae
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C. Greither, Radan Kučera (2008)
Acta Arithmetica
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P. D. T. A. Elliott (1976)
Colloquium Mathematicae
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András Biró (2003)
Acta Arithmetica
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Sebastian Hebda (2013)
Colloquium Mathematicae
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We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.
G. Grekos, L. Haddad, C. Helou, J. Pihko (2005)
Acta Arithmetica
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R. Dacić (1971)
Matematički Vesnik
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Torossian, Charles (2002)
Journal of Lie Theory
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József Balogh, John Lenz, Hehui Wu (2011)
Discussiones Mathematicae Graph Theory
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The Hadwiger number h(G) of a graph G is the maximum size of a complete minor of G. Hadwiger's Conjecture states that h(G) ≥ χ(G). Since χ(G) α(G) ≥ |V(G)|, Hadwiger's Conjecture implies that α(G) h(G) ≥ |V(G)|. We show that (2α(G) - ⌈log_{τ}(τα(G)/2)⌉) h(G) ≥ |V(G)| where τ ≍ 6.83. For graphs with α(G) ≥ 14, this improves on a recent result of Kawarabayashi and Song who showed (2α(G) - 2) h(G) ≥ |V(G) | when α(G) ≥ 3.
Bostjan Bresar (2001)
Discussiones Mathematicae Graph Theory
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A dominating set D for a graph G is a subset of V(G) such that any vertex in V(G)-D has a neighbor in D, and a domination number γ(G) is the size of a minimum dominating set for G. For the Cartesian product G ⃞ H Vizing's conjecture [10] states that γ(G ⃞ H) ≥ γ(G)γ(H) for every pair of graphs G,H. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when γ(G) = γ(H) = 3.
Shanta Laishram, T. N. Shorey (2012)
Acta Arithmetica
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Bert Hartnell, Douglas F. Rall (1995)
Discussiones Mathematicae Graph Theory
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The domination number of a graph G is the smallest order, γ(G), of a dominating set for G. A conjecture of V. G. Vizing [5] states that for every pair of graphs G and H, γ(G☐H) ≥ γ(G)γ(H), where G☐H denotes the Cartesian product of G and H. We show that if the vertex set of G can be partitioned in a certain way then the above inequality holds for every graph H. The class of graphs G which have this type of partitioning includes those whose 2-packing number is no smaller than γ(G)-1 as...
Yan Li, Lianrong Ma (2008)
Acta Arithmetica
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