论文标题
混合笼子：单调，连通性和上限
Mixed Cages: monotony, connectivity and upper bounds
论文作者
论文摘要
a \ emph {$ [z，r; g] $ - 混合笼子}是一个混合图$ z $ - 由弧线进行，$ r $ - 划分为边缘，带有围墙$ g $和最低订单。 ％在本文中我们研究混合笼的结构特性：让$ n [z，r; g] $表示$ [z，r; g] $ - 混合笼的顺序。在本文中，我们证明$ n [z，r; g] $是一个单调的函数，对于$ g $，对于$ z \ in \ {1,2 \} $，我们用它来证明$ [z，r; g] $ - 混合笼子的基础图是2个连接的，$ z \ in \ in \ in \ in \ in \ c} $} $ {1,2,2 $} $ {1,2,2,2 $}。我们还证明$ [z，r; g] $ - 混合笼子连接很强。我们提供$ n [z，r; g] $的界限和$ [z，r; 5] $ - 混合图的构造，并显示$ [10,3; 5] $ - 混合订单$ 50 $的混合笼。
A \emph{$[z, r; g]$-mixed cage} is a mixed graph $z$-regular by arcs, $r$-regular by edges, with girth $g$ and minimum order. %In this paper we study structural properties of mixed cages: Let $n[z,r;g]$ denote the order of a $[z,r;g]$-mixed cage. In this paper we prove that $n[z,r;g]$ is a monotonicity function, with respect of $g$, for $z\in \{1,2\}$, and we use it to prove that the underlying graph of a $[z,r;g]$-mixed cage is 2-connected, for $z\in \{1,2\}$. We also prove that $[z,r;g]$-mixed cages are strong connected. We present bounds of $n[z,r;g]$ and constructions of $[z,r;5]$-mixed graphs and show a $[10,3;5]$-mixed cage of order $50$.
