Related papers: Inversion dans les tournois
A diamond is a $4$-tournament which consists of a vertex dominating or dominated by a $3$-cycle. Assuming the existence of skew-conference matrices, we give a complete characterization of $n$-tournaments with the maximum number of diamonds…
Bermond and Thomassen conjectured in 1981 that every digraph with minimum outdegree at least $2k-1$ contains $k$ vertex-disjoint cycles,here $k$ is a positive integer. Lichiardopol conjectured in 2014 that for every positive integer $k$…
An inverse cascade - energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and…
A Walecki tournament is any tournament that can be formed by choosing an orientation for each of the Hamilton cycles in the Walecki decomposition of a complete graph on an odd number of vertices. In this paper, we show that if some arc in a…
A tournament is a complete directed graph. A king in a tournament is a vertex v such that every other vertex is reachable from v via a path of length at most 2. It is well known that every tournament has at least one king, one of which is a…
We prove that isomorphism of tournaments of twin width at most $k$ can be decided in time $k^{O(\log k)}n^{O(1)}$. This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in…
A $k$-tournament $H$ on $n$ vertices is a pair $(V, A)$ for $2\leq k\leq n$, where $V(H)$ is a set of vertices, and $A(H)$ is a set of all possible $k$-tuples of vertices, such that for any $k$-subset $S$ of $V$, $A(H)$ contains exactly one…
We consider a general round-robin tournament model with equally strong players in which $X_{ij}$ denotes the score of player $i$ against player $j$. We assume that $X_{ij}$ takes values in a countable subset of $[0,1]$ and satisfies…
In the Feedback Arc Set in Tournaments (Subset-FAST) problem, we are given a tournament $D$ and a positive integer $k$, and the objective is to determine whether there exists an arc set $S \subseteq A(D)$ of size at most $k$ whose removal…
An oriented tree $T$ on $n$ vertices is unavoidable if every tournament on $n$ vertices contains a copy of $T$. In this paper we give a sufficient condition for $T$ to be unavoidable, and use this to prove that almost all labelled oriented…
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…
Ryser proved that any two tournaments with the same score sequence are $C_3$-equivalent while Beineke and Moon proved the $C_4$-equivalence for any two bipartite tournaments with the same score lists. In this paper, we extend these results…
Sumner's universal tournament conjecture states that every $(2n-2)$-vertex tournament should contain a copy of every $n$-vertex oriented tree. If we know the number of leaves of an oriented tree, or its maximum degree, can we guarantee a…
The Bermond-Thomassen conjecture states that, for any positive integer $r$, a digraph of minimum out-degree at least $2r-1$ contains at least $r$ vertex-disjoint directed cycles. In 2014, Bang-Jensen, Bessy and Thomass\' e proved the…
A cycle C={v_1,v_2,....,v_1} in a tournament T is said to be even, if when walking along C, an even number of edges point in the wrong direction, that is, they are directed from v_{i+1} to v_i. In this short paper, we show that for every…
Gishboliner, Krivelevich, and Michaeli (2023) conjectured the following generalization of Dirac's theorem: If the minimum degree $\delta$ of an $n$-vertex oriented graph $G$ is greater or equal to $n/2$, then $G$ has a Hamilton oriented…
A non-empty subset $S$ of the vertices of a digraph $D$ is called a {\it safe set} if \begin{itemize} \item[(i)] for every strongly connected component $M$ of $D-S$, there exists a strongly connected component $N$ of $D[S]$ such that there…
For a tournament $H$ with $h$ vertices, its typical density is $h!2^{-\binom{h}{2}}/aut(H)$, i.e. this is the expected density of $H$ in a random tournament. A family ${\mathcal F}$ of $h$-vertex tournaments is {\em dominant} if for all…
A square of a path on $k$ vertices is a directed path $x_1\ldots x_k$, where $x_i$ is directed to $x_{i+2}$, for every $i\in \{1,\ldots, k-1\}$. Recently, Yuster showed that any tournament on $n$ vertices contains a square of a path of…
A $k$-hypertournament $H$ on $n$ vertices is a pair $(V(H),A(H))$, where $V(H)$ is a set of vertices and $A(H)$ is a set of $k$-tuples of vertices, called arcs, such that for any $k$-subset $S$ of $V(H)$, $A(H)$ contains exactly one of the…