We show that cr(G) ≤ 2 iocr(G) 2 settling an open problem of Pach and T´oth [4, 1]. Moreover, iocr(G) = cr(G) if iocr(G) ≤ 2. 1 Crossing Numbers Pach and T´oth point out in ...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
Serious concerns on privacy protection in social networks have been raised in recent years; however, research in this area is still in its infancy. The problem is challenging due ...
Background: Biomedical and chemical databases are large and rapidly growing in size. Graphs naturally model such kinds of data. To fully exploit the wealth of information in these...
We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince a refe...
Peter J. Cameron, Ashley Montanaro, Michael W. New...
A graph G is well-covered if every maximal independent set has the same cardinality. Let sk denote the number of independent sets of cardinality k, and define the independence pol...