Decomposing graphs into edges and triangles
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2019-03-13
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Lidicky, Bernard
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Mathematics
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Mathematics
Abstract
We prove the following 30 year-old conjecture of Győri and Tuza: the edges of every n-vertex graph G can be decomposed into complete graphs C1,. . .,Cℓ of orders two and three such that |C1|+···+|Cℓ| ≤ (1/2+o(1))n2. This result implies the asymptotic version of the old result of Erdős, Goodman and Pósa that asserts the existence of such a decomposition with ℓ ≤ n2/4.
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This is a manuscript of an an article published as D. Král', B. Lidický, T. L. Martins, Y. Pehova. Decomposing Graphs into Edges and Triangles. Combinatorics, Probability and Computing (2019), doi: 10.1017/S0963548318000421. Posted with permission.
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Tue Jan 01 00:00:00 UTC 2019