Related papers: On tournaments combinatorics
This paper is a survey of persistent homology, primarily as it is used in topological data analysis. It includes the theory of persistence modules, as well as stability theorems for persistence barcodes, generalized persistence,…
The celebrated Erd\"{o}s-Hajnal conjecture states that for every undirected graph $H$ there exists $ \epsilon(H) > 0 $ such that every undirected graph on $ n $ vertices that does not contain $H$ as an induced subgraph contains a clique or…
We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…
We determine the inducibility of all tournaments with at most $4$ vertices together with the extremal constructions. The $4$-vertex tournament containing an oriented $C_3$ and one source vertex has a particularly interesting extremal…
Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction…
We present a proof of the extension property for partial automorphisms (EPPA) for classes of finite $n$-partite tournaments for $n \in \{2,3,\ldots,\omega\}$, and for the class of finite semigeneric tournaments. We also prove that the…
Thomason [$\textit{Trans. Amer. Math. Soc.}$ 296.1 (1986)] proved that every sufficiently large tournament contains Hamilton paths and cycles with all possible orientations, except possibly the consistently oriented Hamilton cycle. This…
We give a new and short proof of a theorem on k-hypertournament losing scores due to Zhou et al. [G. Zhou, T. Yao, K. Zhang, On score sequences of k-tournaments, European J. Comb., 21, 8 (2000) 993-1000.]
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In…
We explore the recent results announced in "Robust machine learning by median-of-means: theory and practice" by G. Lecu\'e and M. Lerasle. We show that these results are, in fact, almost obvious outcomes of the machinery developed in [4]…
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…
We study variants of Sidorenko's conjecture in tournaments, where new phenomena arise that do not have clear analogues in the setting of undirected graphs. We first consider oriented graphs that are systematically under-represented in…
Continuing the program begun in the first paper of this series, we present a pair of non-reconstructable tournament on $p$ vertices for each $p=2^n \ge 4$.
We introduce the notion of clique number of a tournament and investigate its relation with the dichromatic number. In particular, it permits defining $\dic$-bounded classes of tournaments, which is the paper's main topic.
This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…
In this paper, we extend the notion of directed clique complex to quivers and introduce an associated homology theory. By applying this construction to biquandle coloring quivers, we obtain new invariants of links. We then introduce a…
Based on known methods for computing the number of distinct score sequences for $n$-vertex tournaments, we develop algorithms for computing the number of distinct score sequences for self-complementary tournaments, strong tournaments, and…
We investigate tournaments with a specified score vector having additional structure: loopy tournaments in which loops are allowed, Hankel tournaments which are tournaments symmetric about the Hankel diagonal (the anti-diagonal), and…
This is the author's PhD thesis, as submitted to the Princeton University. The results of this paper have already appeared in arXiv:math/0607777v4, arXiv:math/0607691 and arXiv:0901.2156.