不同種類的立方漢米爾頓圖

Abstract

令U為連通的平面的立方漢米爾頓圖所成之集合，A為U中所有漢米爾頓的單點漢米爾頓圖所成之集合，B為U中所有單邊漢米爾頓圖所成之集合，C為U中所有漢米爾頓連通圖所成之集合。根據集合A、B與C互斥與交集的運算，U被分成8個集合。在這一篇文章中我將要證明這8個集合為無限的。

Let U be the set of connected planar cubic hamiltonian graphs, A be the set of hamiltonian 1-vertex hamiltonian graphs in U, B be the set of 1-edge hamiltonian graphs in U, and C be the set of hamiltonian connected graphs in U. With the and/or exclusion of the sets A,B, and C, U is divided into eight subsets. In this paper, we prove that there are infinitely many elements in each of the eight subsets.