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Large triangle packings and Tuza’s conjecture in sparse random graphs
Combinatorics, Probability and Computing ( IF 0.9 ) Pub Date : 2020-07-22 , DOI: 10.1017/s0963548320000115 Patrick Bennett , Andrzej Dudek , Shira Zerbib
Combinatorics, Probability and Computing ( IF 0.9 ) Pub Date : 2020-07-22 , DOI: 10.1017/s0963548320000115 Patrick Bennett , Andrzej Dudek , Shira Zerbib
The triangle packing number v (G ) of a graph G is the maximum size of a set of edge-disjoint triangles in G . Tuza conjectured that in any graph G there exists a set of at most 2v (G ) edges intersecting every triangle in G . We show that Tuza’s conjecture holds in the random graph G = G (n , m ), when m ⩽ 0.2403n 3/2 or m ⩾ 2.1243n 3/2 . This is done by analysing a greedy algorithm for finding large triangle packings in random graphs.
中文翻译:
稀疏随机图中的大三角形堆积和Tuza猜想
三角包装号v (G ) 的图G 是一组边不相交三角形的最大尺寸G . Tuza 推测在任何图中G 最多存在一组 2v (G ) 边与中的每个三角形相交G . 我们证明 Tuza 猜想在随机图中成立G =G (n ,米 ), 什么时候米 ⩽ 0.2403n 3/2 要么米 ⩾ 2.1243n 3/2 . 这是通过分析用于在随机图中查找大三角形填充的贪心算法来完成的。
更新日期:2020-07-22
中文翻译:
稀疏随机图中的大三角形堆积和Tuza猜想
三角包装号