论文标题
近均匀锦标赛的建筑，扩展和路径
Construction, Extension and Paths of Near-Homogeneous Tournaments
论文作者
论文摘要
同质锦标赛是一项锦标赛，其$ 4T+3 $顶点，因此每个弧都完全包含在$ t+1 $ 1 $长度的$ 3 $中。同质锦标赛是第一类比赛，被证明是可扩展的路径，这意味着，在这样的比赛中，每个非汉顿路径$ p $ t $都可以扩展到具有相同初始和终端顶点的路径$ p'$，并且$ v（p'p'p）= v（p）\ cup \ cup \ \ \ \ \ \ \ \ \ for a Back for a sterte vertes $ v（p）$。为了找到更多的可扩展比赛，我们研究了称为近均匀锦标赛的同质比赛的概括，其中每个弧都包含在$ t $ t $或$ t+1 $ $ 3 $ 3 $中。在$ 4T+1 $顶点的比赛中定义了接近同质的性。在本文中，我们提出了一种新方法，以$ 4T+1 $顶点构建近均匀的比赛。然后，我们证明，近均匀锦标赛的定义可以扩展到具有偶数顶点的比赛。最后，我们验证了近均匀锦标赛的路径可扩展性，从而扩展了可扩展比赛的类别。
A homogeneous tournament is a tournament with $4t+3$ vertices such that every arc is contained in exactly $t+1$ cycles of length $3$. Homogeneous tournaments are the first class of tournaments that are proved to be path extendable, which means that every nonhamiltonian path $P$ in such a tournament $T$ can be extended to a path $P'$ with the same initial and terminal vertex and $V(P')=V(P)\cup \{u\}$ for a certain vertex $u\in V(T)\backslash V(P)$. In order to find more path extendable tournaments we study the generalization of homogeneous tournaments called near-homogeneous tournaments, in which every arc is contained in $t$ or $t+1$ cycles of length $3$. Near-homogeneity has been defined in tournaments with $4t+1$ vertices. In this paper, we raise a new method to construct near-homogeneous tournaments with $4t+1$ vertices. We then show that the definition of near-homogeneous tournament can be extended to tournaments with an even number of vertices. Finally we verify path extendability of near-homogeneous tournaments, thus expand the class of path extendable tournaments.
