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Ingo Schiermeyer, Mariusz Woźniak (2007)
Discussiones Mathematicae Graph Theory
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For a graph G of order n we consider the unique partition of its vertex set V(G) = A ∪ B with A = {v ∈ V(G): d(v) ≥ n/2} and B = {v ∈ V(G):d(v) < n/2}. Imposing conditions on the vertices of the set B we obtain new sufficient conditions for hamiltonian and pancyclic graphs.
Hoang, C.T., Le, V.B. (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [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.
Ngo Dac Tan, Le Xuan Hung (2004)
Discussiones Mathematicae Graph Theory
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A graph G is called a split graph if the vertex-set V of G can be partitioned into two subsets V₁ and V₂ such that the subgraphs of G induced by V₁ and V₂ are empty and complete, respectively. In this paper, we characterize hamiltonian graphs in the class of split graphs with minimum degree δ at least |V₁| - 2.
Jaroslav Ivanco (2007)
Discussiones Mathematicae Graph Theory
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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
(1975)
Czechoslovak Mathematical Journal
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Chandran, L.Sunil, Lozin, Vadim V., Subramanian, C.R. (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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