Original scientific paper

Total forcing number of the triangular grid

D. Vukičević
J. Sedlar

Abstract

Let $T$ be a square triangular grid with $n$ rows and columns of vertices and $n$ an even number. A set of edges $E\subset E(T)$ completely determines perfect matchings on $T$ if there are no two different matchings on $T$ coinciding on $E.$ We establish the upper and the lower bound for the smallest value of $\left| E\right| ,$ i.e. we show that
\begin{equation*}
\frac{5}{4}n^{2}-\frac{21}{2}n+\frac{41}{4}\leq \left| E\right| \leq \frac{5}{4}n^{2}+n-2
\end{equation*}%
and show that $\left| E\right| /\left| E(T)\right| $ tends
to $5/12$ when $n$ tends to infinity.

Keywords

forcing matchings; total forcing matchings; grid; triangular grid; extremal problem

Hrčak ID:

685

URI

https://hrcak.srce.hr/685

Publication date:

22.12.2004.

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