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DAM
2008
67views more  DAM 2008»
15 years 5 months ago
On the variance of Shannon products of graphs
We study the combinatorial problem of finding an arrangement of distinct integers into the ddimensional N-cube so that the maximal variance of the numbers on each -dimensional sec...
József Balogh, Clifford D. Smyth
DM
2008
88views more  DM 2008»
15 years 5 months ago
Lower bounding the boundary of a graph in terms of its maximum or minimum degree
A vertex v of a graph G is a boundary vertex if there exists a vertex u such that the distance in G from u to v is at least the distance from u to any neighbour of v. We give the ...
Tobias Müller, Attila Pór, Jean-S&eacu...
DM
2006
121views more  DM 2006»
15 years 5 months ago
The acircuitic directed star arboricity of subcubic graphs is at most four
A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented grap...
Alexandre Pinlou, Eric Sopena
JGT
2006
40views more  JGT 2006»
15 years 5 months ago
How many graphs are unions of k-cliques?
We study the number F[n; k] of n-vertex graphs that can be written as the edgeunion of k-vertex cliques. We obtain reasonably tight estimates for F[n; k] in the cases (i) k = n-o(...
Béla Bollobás, Graham Brightwell
WG
2010
Springer
15 years 3 months ago
Graphs that Admit Right Angle Crossing Drawings
We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a ...
Karin Arikushi, Radoslav Fulek, Balázs Kesz...