On a combinatorial game
Paul Erdös,J. L. Selfridge +1 more
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TLDR
A drawing strategy is explained which applies to a wide class of combinatorial and positional games and when applied to n -dimensional Tic-Tac-Toe, it improves a result of Hales and Jewett.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-05-01 and is currently open access. It has received 346 citations till now. The article focuses on the topics: Combinatorial explosion & Combinatorial principles.read more
Citations
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The Probabilistic Method
TL;DR: A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
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Graph Coloring Problems
Tommy R. Jensen,Bjarne Toft +1 more
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
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The Design of Approximation Algorithms
TL;DR: In this paper, the authors present a survey of the central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization.
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Approximation algorithms for facility location problems
TL;DR: This note is intended as companion to the lecture at CONF 2000, mainly to give pointers to the appropriate references.
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A survey and critique of multiagent deep reinforcement learning
TL;DR: In this paper, the authors provide a clear overview of current multi-agent deep reinforcement learning (MDRL) literature, and provide general guidelines to new practitioners in the area: describing lessons learned from MDRL works, pointing to recent benchmarks, and outlining open avenues of research.
References
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A combinatorial problem in geometry
P. Erdös,G. Szekeres +1 more
TL;DR: In this paper, the present problem has been suggested by Miss Esther Klein in connection with the following proposition: "Our present problem is the same problem as the one suggested by the author of this paper."
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Some remarks on the theory of graphs
TL;DR: In this paper, a special case of a theorem of Ramsey can be stated in graph theoretic language as follows: there exists a function f(k, I) of positive integers k, I with the following property.
Journal ArticleDOI
Regularity and Positional Games
A. W. Hales,R. I. Jewett +1 more
TL;DR: In this paper, it was shown that a set is n-regular in X if, for any partition of X into N parts, some part has as a subset a member of the set.