论文标题
Tuza的随机图猜想
Tuza's Conjecture for random graphs
论文作者
论文摘要
ZS的著名猜想。图扎说，在任何（有限）图中，边缘的三角形盖的最小尺寸最多是一组边缘 - 迪斯连接三角形的最大尺寸的两倍。解决了贝内特，杜德克和Zerbib的最新问题，我们证明这对于随机图是正确的。更精确： \ [\ mbox {对于任何$ p = p = p（n）$，$ \ mathbb p（\ mbox {$ g_ {n，p} $满足Tuza的comenture}）\ rightarrow 1 $（as $ n \ rightArrow \ rightArrow \ rightArrow \ infty \ infty \ infty $）。
A celebrated conjecture of Zs. Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. Resolving a recent question of Bennett, Dudek, and Zerbib, we show that this is true for random graphs; more precisely: \[ \mbox{for any $p=p(n)$, $\mathbb P(\mbox{$G_{n,p}$ satisfies Tuza's Conjecture})\rightarrow 1 $ (as $n\rightarrow\infty$).} \]
