Caro, Lauri, and Zarb's forest bound conjecture for f2f_2

From papers

Let tt be a positive integer and let FF be a forest. For a graph GG, let fk(G)f_k(G) be the minimum cardinality of a set XX of vertices of GG such that GXG-X has either kk vertices of maximum degree or order less than kk.

Caro, Lauri, and Zarb's conjecture. If FF has order at most

16(t3+6t2+17t+12),\frac{1}{6}\left(t^3+6t^2+17t+12\right),

then

f2(F)t.f_2(F)\leq t.

This is a precise conjecture for forests that improves the known general forest bound and was constructed to be tight by matching examples. The paper states that it verifies this conjecture.

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Sources & referencesView supporting material

Primary source

M. Fürst, M. Gentner, M. A. Henning, S. Jäger and D. Rautenbach, “Equating k Maximum Degrees in Graphs without Short Cycles”, arXiv:1705.07409 (2017).

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