Cycle intersection graphs and minimum decycling sets of even graphs

被引:1
|
作者
Cary, Michael [1 ]
机构
[1] West Virginia Univ, Ctr Alternat Fuels Engines & Emiss, Morgantown, WV 26506 USA
关键词
Decycling; decycling number; even graph; spanning tree; cycle rank; NUMBER;
D O I
10.1142/S1793830920500275
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling number of all even graphs. This bound is shown to be significantly better when an even graph admits a cycle decomposition in which any two cycles intersect in at most one vertex. Links between the cycle rank of the cycle intersection graph of an even graph and the decycling number of the even graph itself are found. The problem of choosing an ideal cycle decomposition is addressed and is presented as an optimization problem over the space of cycle decompositions of even graphs, and we conjecture that the upper bound for the decycling number of even graphs presented in this paper is best possible.
引用
收藏
页数:12
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