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arXiv · 1601.01211

Density of 4-edge paths in graphs with fixed edge density

Dániel T. Nagy
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Abstract

We investigate the number of 4-edge paths in graphs with a fixed number of vertices and edges. An asymptotically sharp upper bound is given to this quantity. The extremal construction is the quasi-star or the quasi-clique graph, depending on the edge density. An easy lower bound is also proved. This answer resembles the classic theorem of Ahlswede and Katona about the maximal number of 2-edge paths, and a recent theorem of Kenyon, Radin, Ren and Sadun about k-edge stars.

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Dániel T. Nagy. 2016-01-06. Density of 4-edge paths in graphs with fixed edge density. https://arxiv.org/abs/1601.01211

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