Embeddings of Graphs in Euclidean Spaces.
J. Reiterman, V Rödl, E. Sinajová (1989)
Discrete & computational geometry
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J. Reiterman, V Rödl, E. Sinajová (1989)
Discrete & computational geometry
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D.P. Dobkin, S.J. Friedman, K.J. Supowit (1990)
Discrete & computational geometry
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Bretto, A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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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.
W. Wessel (1987)
Applicationes Mathematicae
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Gary Chartrand, Hudson V. Kronk, Seymour Schuster (1973)
Colloquium Mathematicae
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Zdzisław Skupień (2007)
Discussiones Mathematicae Graph Theory
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Risto Šokarovski (1977)
Publications de l'Institut Mathématique
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H. Maehara (1991)
Discrete & computational geometry
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