环面方格图Ⅰ.不可收缩圈的性质

On the Property of Noncontractible Cycles of the Toroidal Square Grid Graphs I.

图论中研究的方格图有很好的物理和化学背景,在文献[1-3]中Ridlle,Afshani和Kleinerman等人先后研究了C_(2m)×C_(2n)的匹配强迫数,本文对C_(2m)×C_(2n)进行扩充,增加了一个旋转参数t,首次定义了环面方格图S(p,q,t),并得到S(p,q,t)上部分不可收缩圈的结构性质,为研究其匹配强迫数奠定了一定的理论基础.

The study on grid graphs in graph theory has excellent background in statistical physics and chemistry. On the studies of [1-3], Riddle, Afshani and Kleinerman researched into the forcing matching number of f（C2m ×C2n） = 2n. In this paper, we expand C2m × C2n with a rotation parameter t. Besides, we define the toroidal grid graph S （p, q, t） for the first time, and present its structural properties of noncontractible circles, which will lay a theoretical foundation for studying its forcing matching number.