Physiological characteristics of eosinophilic esophagitis

Király, Á

doi:10.1055/s-0032-1312391

Cited by 3 publications

(3 citation statements)

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“…Recently András Frank asked what we know about partitioning the edge set of a graph into k (not necessarily spanning) trees. One can easily see that whether a simple graph is a tree or not is in P. It was shown by Király that the problem of deciding if the edge set of a simple graph is the disjoint union of three trees is NPcomplete by reducing the 3-colorability problem to it [3]. Now we prove that for two trees the problem is also NP-complete.…”

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confidence: 79%

Partitioning to three matchings of given size is NP-complete for bipartite graphs

Pálvölgyi

2014

Acta Universitatis Sapientiae, Informatica

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confidence: 79%

Partitioning to three matchings of given size is NP-complete for bipartite graphs

Pálvölgyi

2014

Acta Universitatis Sapientiae, Informatica

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“…For d = 2, there is a simple proof by Zoltán Király [9], who also invented the above formulation of the problem. We do not have strong evidence for this conjecture to be true, but it is mathoverflow-hard.…”

Section: Possible Further Improvements and Remarksmentioning

confidence: 99%

Asymptotically Optimal Pairing Strategy for Tic-Tac-Toe with Numerous Directions

Mukkamala¹,

Pálvölgyi²

2010

Electron. J. Combin.

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We show that there is an m = 2n + o(n), such that, in the Maker-Breaker game played on Z d where Maker needs to put at least m of his marks consecutively in one of n given winning directions, Breaker can force a draw using a pairing strategy. This improves the result of Kruczek and Sundberg [12] who showed that such a pairing strategy exits if m ≥ 3n. A simple argument shows that m has to be at least 2n + 1 if Breaker is only allowed to use a pairing strategy, thus the main term of our bound is optimal.

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“…• covering a symmetric crossing supermodular set function by a uniform hypergraph [26], • covering a symmetric skew-supermodular set function by a graph (this problem is NP-complete [27]), • covering a symmetric semi-monotone set function by a graph [20], • covering a symmetric skew-supermodular set function by a hypergraph of minimum total size [31].…”

Section: The First Part Contains the Following Generalizations In Gramentioning

confidence: 99%

Edge-Connectivity Augmentations of Graphs and Hypergraphs

Szigeti

Research Trends in Combinatorial Optimization

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Summary.A. Frank (Augmenting graphs to meet edge-connectivity requirements, SIAM J. on Disc. Math. Vol. 5, No. 1 (1992) 22-53) developed a method to solve edge-connectivity augmentation problems. His paper has stimulated further research in a number of directions, including many interesting generalizations.This paper surveys the current State of the Art on the edge-connectivity augmentation problem. Recent extensions of the problem are presented for undirected graphs, hypergraphs and more generally for set functions. Shortened proofs are provided for some of the results. A list of open problems is also presented.

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Physiological characteristics of eosinophilic esophagitis

Cited by 3 publications

References 0 publications

Partitioning to three matchings of given size is NP-complete for bipartite graphs

Partitioning to three matchings of given size is NP-complete for bipartite graphs

Asymptotically Optimal Pairing Strategy for Tic-Tac-Toe with Numerous Directions

Edge-Connectivity Augmentations of Graphs and Hypergraphs

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