Listing All Fixed-Length Simple Cycles in Sparse Graphs in Optimal Time

被引：2
|
作者：
Manoussakis, George [1 ]
机构：
[1] Univ Paris Saclay, Univ Paris Sud, CNRS, LRI, F-91405 Orsay, France
来源：
FUNDAMENTALS OF COMPUTATION THEORY, FCT 2017 | 2017年 / 10472卷
关键词：
Sparse graphs; k-degenerate; Fixed-size cycles listing; PLANAR; ARBORICITY;
D O I：
10.1007/978-3-662-55751-8_28
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The degeneracy of an n-vertex graph G is the smallest number k such that every subgraph of G contains a vertex of degree at most k. We present an algorithm for enumerating all simple cycles of length p in an n-order k-degenerate graph running in time O(n([p/2]) k([p/2])). We then show that this algorithm is worst-case output size optimal by proving a T(n([p/2]) k([p/2])) bound on the maximal number of simple p-length cycles in these graphs. Our results also apply to induced (chordless) cycles.
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页码：355 / 366
页数：12
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