Partially critical tournaments and partially critical supports

摘要: Given a tournament $T=(V,A)$, with each subset $X$ of $V$ is associated the subtournament $T[X]=(X,A\cap (X\times X))$ $T$ induced by $X$. A $I$ is an interval $T$ provided that for any $a,b\in I$ and $x\in V\setminus I$, $(a,x)\in A$ if and only if $(b,x)\in A$. For example, $\emptyset$, $\{x\}$, where $x\in V$, are intervals called \emph{trivial}. A tournament indecomposable all its trivial; otherwise, it decomposable. Let $T=(V,A)$ be indecomposable tournament. The \emph{critical} every $x\in $T[V\setminus\{x\}]$ It is \emph{partially critical} there exists proper of $V$ such that $| X| \geq 3$, $T[X]$ indecomposable and every X$, is decomposable. partially critical tournaments are characterized. Lastly, given consider $X$ $|X|\geq 3$ indecomposable. The support according to family $x\in X$ and $T[V\setminus\{x,y\}]$ decomposable $y\in (V\setminus X)\setminus\{x\}$. It shown contains at most three vertices. whose supports contain least two vertices characterized.