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DAM
2007
141views more  DAM 2007»
13 years 5 months ago
On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into packings with pairwise different widths. Several...
Bostjan Bresar, Sandi Klavzar, Douglas F. Rall
APPML
2011
13 years 11 days ago
The fractional chromatic number of Zykov products of graphs
Zykov designed one of the oldest known family of triangle-free graphs with arbitrarily high chromatic number. We determine the fractional chromatic number of the Zykov product of ...
Pierre Charbit, Jean-Sébastien Sereni
SIAMDM
2008
154views more  SIAMDM 2008»
13 years 5 months ago
On the First-Fit Chromatic Number of Graphs
The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the max...
József Balogh, Stephen G. Hartke, Qi Liu, G...
IPL
2006
105views more  IPL 2006»
13 years 5 months ago
Finding and counting cliques and independent sets in r-uniform hypergraphs
We present a matrix multiplication based algorithm for counting the number of (induced) occurrences of a fixed r-uniform hypergraph in a larger hypergraph. In many cases, the runn...
Raphael Yuster
CORR
2010
Springer
168views Education» more  CORR 2010»
13 years 5 months ago
Upper oriented chromatic number of undirected graphs and oriented colorings of product graphs
The oriented chromatic number of an oriented graph G is the minimum order of an oriented graph H such that G admits a homomorphism to H. The oriented chromatic number of an undire...
Eric Sopena