665 research outputs found
The Incidence Chromatic Number of Toroidal Grids
An incidence in a graph is a pair with and , such that and are incident. Two incidences and
are adjacent if , or , or the edge equals or . The
incidence chromatic number of is the smallest for which there exists a
mapping from the set of incidences of to a set of colors that assigns
distinct colors to adjacent incidences. In this paper, we prove that the
incidence chromatic number of the toroidal grid equals 5
when and 6 otherwise.Comment: 16 page
Knapsack problem with objective value gaps
International audienceWe study a 0-1 knapsack problem, in which the objective value is forbidden to take some values. We call gaps related forbidden intervals. The problem is NP-hard and pseudo-polynomially solvable independently on the measure of gaps. If the gaps are large, then the problem is polynomially non-approximable. A non-trivial special case with respect to the approximate solution appears when the gaps are small and polynomially close to zero. For this case, two fully polynomial time approximation schemes are proposed. The results can be extended for the constrained longest path problem and other combinatorial problems
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