Upper bounds for the span in triangular lattice graphs: application to frequency planning for cellular network

Abstract : We study a problem coming from the design of wireless cellular radiocommunication network. Frequency planning constraints are modelled in terms of graph theory. For each planning function $f$ let us call $sp(f)$ - or the {\em span} of the frequency planning $f$ - the difference between the largest and the smallest frequency used. Let the {\em Order} of the graph be $Or(G)=sp(G)+1$ and the {\em maximal local order} of the graph the maximum order of a clique of $G$, i.e. $Mlo(G) = \max_{X \ \mbox{clique of}\ G} sp(X)$. We show: $Mlo(G) \leq sp(G) \leq 8\lceil\frac{Mlo(G)}{6}\rceil$.
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Stephane Ubeda, Janez Zerovnik. Upper bounds for the span in triangular lattice graphs: application to frequency planning for cellular network. [Research Report] LIP RR-1997-28, Laboratoire de l'informatique du parallélisme. 1997, 2+15p. ⟨hal-02102069⟩

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