一类4-正则图的最小折数纵横扩张

MINIMIZATION OF RECTILINEAR EXTENTIONS OF A KIND OF 4-REGULAR GRAPHS

纵横嵌入是图论中的一个有很强应用背景的问题 .作为其基本的一步就是研究一个嵌入的纵横扩张 .虽然确定最小折数扩张已经从理论上得到了解答 ,但并未给出很好的算法 .本文提供了这方面的一些结论 ,并进一步研究了一类 4_正则图G,得到了确定这类图最小折数纵横扩张的一个线性算法 .

Rectilinear embedding can be applied to social life . It can, in principle, be obtained from a rectilinear extension of a graph on the plane. Although the problem for determining a rectilinear extension of a graph with the minimum total number of bends has been solved in theory, there is no a good algorithm. We demostrates some results in this paper and a linear time algorithm is designed to get a rectilinear extension of a kind of 4-regular graphs with the minimum total number of bends.