Densities of minor-closed graph families.
Eppstein, David (2010)
The Electronic Journal of Combinatorics [electronic only]
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Eppstein, David (2010)
The Electronic Journal of Combinatorics [electronic only]
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Ken-ichi Kawarabayashi (2004)
Discussiones Mathematicae Graph Theory
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Let G be a graph of order n. Let K¯ₗ be the graph obtained from Kₗ by removing one edge. In this paper, we propose the following conjecture: Let G be a graph of order n ≥ lk with δ(G) ≥ (n-k+1)(l-3)/(l-2)+k-1. Then G has k vertex-disjoint K¯ₗ. This conjecture is motivated by Hajnal and Szemerédi's [6] famous theorem. In this paper, we verify this conjecture for l=4.
DeLaViña, Ermelinda, Waller, Bill (2008)
The Electronic Journal of Combinatorics [electronic only]
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Mubayi, Dhruv, Talbot, John (2008)
The Electronic Journal of Combinatorics [electronic only]
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Füredi, Zoltán, Pikhurko, Oleg, Simonovits, Miklós (2003)
The Electronic Journal of Combinatorics [electronic only]
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Nagy, Zoltán Lóránt (2011)
The Electronic Journal of Combinatorics [electronic only]
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Allen, Peter (2010)
The Electronic Journal of Combinatorics [electronic only]
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Mubayi, Dhruv, Zhao, Yi (2003)
The Electronic Journal of Combinatorics [electronic only]
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Marietjie Frick, Frank Bullock (2001)
Discussiones Mathematicae Graph Theory
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The nth detour chromatic number, χₙ(G) of a graph G is the minimum number of colours required to colour the vertices of G such that no path with more than n vertices is monocoloured. The number of vertices in a longest path of G is denoted by τ( G). We conjecture that χₙ(G) ≤ ⎡(τ(G))/n⎤ for every graph G and every n ≥ 1 and we prove results that support the conjecture. We also present some sufficient conditions for a graph to have nth chromatic number at most 2.
Daniel W. Cranston, Sogol Jahanbekam, Douglas B. West (2014)
Discussiones Mathematicae Graph Theory
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The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms...
Alon, Noga, Sudakov, Benny (2006)
The Electronic Journal of Combinatorics [electronic only]
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Wong, P.K. (1985)
International Journal of Mathematics and Mathematical Sciences
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Zsolt Tuza (2005)
Discussiones Mathematicae Graph Theory
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An infinite class of counterexamples is given to a conjecture of Dahme et al. [1] concerning the minimum size of a dominating vertex set that contains at least a prescribed proportion of the neighbors of each vertex not belonging to the set.
Martin, Ryan, Zhao, Yi (2009)
The Electronic Journal of Combinatorics [electronic only]
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Fischer, Eldar (1999)
The Electronic Journal of Combinatorics [electronic only]
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