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Jan Kratochvíl (1995)
Commentationes Mathematicae Universitatis Carolinae
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In this note, we introduce the notion of -Ramsey classes of graphs and we reveal connections to intersection dimensions of graphs.
DeLaVina, Ermelinda, Fajtlowicz, Siemion (1996)
The Electronic Journal of Combinatorics [electronic only]
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Amanda Niedzialomski (2016)
Discussiones Mathematicae Graph Theory
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For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...
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.
Chandran, L.Sunil, Lozin, Vadim V., Subramanian, C.R. (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Yan Yang, Yichao Chen (2017)
Discussiones Mathematicae Graph Theory
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The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study...
Zlatomir Lukić (1982)
Publications de l'Institut Mathématique
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X. Shen, Y. Hou, I. Gutman, X. Hui (2010)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Abdollah Khodkar, Rui Xu (2007)
Discussiones Mathematicae Graph Theory
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In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,an/(a+b) + a - 2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction...
Steve Fisk (1995)
Discussiones Mathematicae Graph Theory
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A homomorphism from one graph to another is a map that sends vertices to vertices and edges to edges. We denote the number of homomorphisms from G to H by |G → H|. If 𝓕 is a collection of graphs, we say that 𝓕 distinguishes graphs G and H if there is some member X of 𝓕 such that |G → X | ≠ |H → X|. 𝓕 is a distinguishing family if it distinguishes all pairs of graphs. We show that various collections of graphs are a distinguishing family.
Brouwer, A.E., Spence, E. (2009)
The Electronic Journal of Combinatorics [electronic only]
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