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Edge coloring, total coloring and L(2,1)-labeling are well-studied NP-hard graph problems. Even the versions asking whether a graph has a coloring with few colors or a labeling with few labels remain NP-hard on graphs of small maximum degree. This paper studies enumeration and counting problems on edge colorings, total colorings and L(2,1)-labelings of(More)
In this thesis we focus on subexponential algorithms for NP-hard graph problems: exact and parameterized algorithms that have a truly subexponential running time behavior. For input instances of size n we study exact algorithms with running time 2 O(√ n) and parameterized algorithms with running time 2 O(√ k) ·n O(1) with parameter k, respectively. We study(More)
A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x = y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. It was shown in [4] that a graph is representable if and only if it is k-representable for some(More)
Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at. In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following(More)
We analyze the complexity status of one of the known discrete optimization problems where the optimization criterium is switched from max to min. In the considered problem, we search in a finite set of Euclidean vectors (points) a subset that minimizes the squared norm of the sum of its elements divided by the cardinality of the subset. It is proved that if(More)
The following problem is considerd: Problem Max-Cut(R q)-SD (Max-Cut in Euclidean space, the case for Squared Distances). Input: A set X = {x 1 ,. .. , x N } of Euclidean vectors R q and positive number A. Question: Is there a partition of the set X into two subsets Y and Z such that y∈Y z∈Z y − z 2 ≥ A? The optimization variant of this problem corresponds(More)
A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x = y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. The minimum k for which a representable graph G is k-representable is called its representation(More)
A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x = y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. Examples of non-representable graphs are found in this paper. Some wide classes of graphs are(More)
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