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NADIR

On the Number of Labeled Graphs of Bounded Treewidth, and some explicit absolute constant .. Disregarding lower-order terms, the gap between the lower and upper bound is of order .. The upper bound is a direct consequence of the well-known formula for the number of labeled .-trees, while the lower bound is obtained from an explicit construction. It fo

Bucket

,Uniquely Restricted Matchings and?Edge?Colorings,d studied in a number of articles. Our contribution is twofold. We provide approximation algorithms for computing a uniquely restricted matching of maximum size in some bipartite graphs. In particular, we achieve a ratio of 5/9 for subcubic bipartite graphs, improving over a 1/2-approximation algori

Conscientious

Defective Coloring on Classes of Perfect Graphs,e show that this natural generalization of . is much harder on several basic graph classes. In particular, we show that it is NP-hard on split graphs, even when one of the two parameters . is set to the smallest possible fixed value that does not trivialize the problem (. or .). Together with a simp

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極力證明

Computing Maximum Cliques in ,-EPG Graphs, graphs where the path on the grid associated to each vertex has at most . bends. Epstein et al. showed in 2013 that computing a maximum clique in .-EPG graphs is polynomial. As remarked in?[Heldt et al. 2014], when the number of bends is at least 4, the class contains 2-interval graphs for which co

ECG769

Intersection Graphs of Rays and Grounded Segments,In particular, we show that:.The first result answers an open problem posed by Cabello and Jej?i?. The third result confirms a conjecture by Cabello. We thereby completely elucidate the remaining open questions on the containment relations between these classes of segment graphs. We further characte

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On ,-Topological Intersection Graphs,ally generalize many important classes of graphs, e.g., interval graphs and circular-arc graphs. Our paper is the first study of the recognition and dominating set problems of this large collection of intersection classes of graphs..We negatively answer the question of Biró, Hujter, and Tuza who ask

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