Davila–Kenter forcing-number conjecture for graphs with given girth

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Let GG be a graph with girth g≥3g\geq 3 and minimum degree δ≥2\delta\geq 2. Its forcing number F(G)F(G) is the cardinality of a smallest forcing set, where a forcing set is an initial set of colored vertices from which the iterative forcing process colors every vertex of GG.

Davila–Kenter conjecture.

F(G)≥δ+(δ−2)(g−3).F(G)\geq \delta+(\delta-2)(g-3).

The conjecture gives a lower bound for the forcing number in terms of minimum degree and girth. The supplied material does not state whether it has been resolved.

References

Primary source

Randy Davila and Michael Henning, “The forcing number of graphs with a given girth”, arXiv:1610.08435 (2016).

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