Author:
Bennett Patrick,Dudek Andrzej,Zerbib Shira
Abstract
AbstractThe 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 ⩽ 0.2403n3/2 or m ⩾ 2.1243n3/2. This is done by analysing a greedy algorithm for finding large triangle packings in random graphs.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference24 articles.
1. On Tail Probabilities for Martingales
2. [23] Wormald, N. (1999) The differential equation method for random graph processes and greedy algorithms. In Lectures on Approximation and Randomized Algorithms (M. Karoński and H. J. Prömel, eds), pp. 73–155, PWN.
3. On a conjecture of Tuza about packing and covering of triangles
4. Near Perfect Coverings in Graphs and Hypergraphs
5. The triangle-free process and R(3,k);Fiz Pontiveros;Mem. Amer. Math. Soc.,2020
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