阈值图的Tuza猜想

Discret. Math. Theor. Comput. Sci. Pub Date : 2021-05-20 DOI:10.46298/dmtcs.7660

Marthe Bonamy, Łukasz Bożyk, Andrzej Grzesik, Meike Hatzel, Tomáš Masařík, Jana Novotn'a, Karolina Okrasa

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引用次数: 3

摘要

图扎在1981年提出了一个著名的猜想，即在一个没有k+1个边不相交三角形的图中，最多删除2k条边就足以得到一个无三角形图。这个猜想适用于树宽较小或最大平均度较小的图，包括平面图。然而，对于既不是团也不是四色的稠密图，只有渐近结果是已知的。这里，我们证实了阈值图的猜想，即同时是分割图和图的图，以及两边都能被4整除的共链图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Tuza's Conjecture for Threshold Graphs

Tuza famously conjectured in 1981 that in a graph without k+1 edge-disjoint triangles, it suffices to delete at most 2k edges to obtain a triangle-free graph. The conjecture holds for graphs with small treewidth or small maximum average degree, including planar graphs. However, for dense graphs that are neither cliques nor 4-colorable, only asymptotic results are known. Here, we confirm the conjecture for threshold graphs, i.e. graphs that are both split graphs and cographs, and for co-chain graphs with both sides of the same size divisible by 4.

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Discret. Math. Theor. Comput. Sci.

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