Constructive lower bounds on classical multicolor Ramsey numbers.
Xu, Xiaodong, Xie, Zheng, Exoo, Geoffrey, Radziszowski, Stanisław P. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Xu, Xiaodong, Xie, Zheng, Exoo, Geoffrey, Radziszowski, Stanisław P. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Elliot Krop, Irina Krop (2013)
Discussiones Mathematicae Graph Theory
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Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás. We show that [...] , slightly improving the bound of Axenovich. We make small improvements on bounds of Erdös and Gyárfás by showing [...] and for all even n ≢ 1(mod 3), f(n, 4, 5) ≤ n− 1. For a complete bipartite graph G= Kn,n, we show an n-color construction to color...
Mubayi, Dhruv (2002)
The Electronic Journal of Combinatorics [electronic only]
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Evelyne Flandrin, Hao Li, Antoni Marczyk, Jean-François Saclé, Mariusz Woźniak (2017)
Discussiones Mathematicae Graph Theory
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A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . . , k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.
Axenovich, Maria, Choi, JiHyeok (2010)
The Electronic Journal of Combinatorics [electronic only]
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Robertson, Aaron (1999)
The Electronic Journal of Combinatorics [electronic only]
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Ward, C., Szabó, S. (1994)
Acta Mathematica Universitatis Comenianae. New Series
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Tomasz Dzido, Renata Zakrzewska (2006)
Discussiones Mathematicae Graph Theory
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The upper domination Ramsey number u(m,n) is the smallest integer p such that every 2-coloring of the edges of Kₚ with color red and blue, Γ(B) ≥ m or Γ(R) ≥ n, where B and R is the subgraph of Kₚ induced by blue and red edges, respectively; Γ(G) is the maximum cardinality of a minimal dominating set of a graph G. In this paper, we show that u(4,4) ≤ 15.
Fujita, Shinya, Kaneko, Atsushi, Schiermeyer, Ingo, Suzuki, Kazuhiro (2009)
The Electronic Journal of Combinatorics [electronic only]
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Richard H. Schelp (2002)
Discussiones Mathematicae Graph Theory
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The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.
Albertson, Michael O., Chappell, Glenn G., Kierstead, H.A., Kündgen, André, Ramamurthi, Radhika (2004)
The Electronic Journal of Combinatorics [electronic only]
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LeSaulnier, Timothy D., Stocker, Christopher, Wenger, Paul S., West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Eric Andrews, Laars Helenius, Daniel Johnston, Jonathon VerWys, Ping Zhang (2014)
Discussiones Mathematicae Graph Theory
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A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph
Gary Chartrand, Futaba Okamoto, Craig W. Rasmussen, Ping Zhang (2009)
Discussiones Mathematicae Graph Theory
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For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs...
Kostochka, Alexandr (2002)
The Electronic Journal of Combinatorics [electronic only]
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