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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Ivica Bošnjak, Rozália Madarász (2018)
Czechoslovak Mathematical Journal
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For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined.