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The strong isometric dimension of a reflexive graph is related to its injective hull: both deal with embedding reflexive graphs in the strong product of paths. We give several upper and lower bounds for the strong isometric dimension of general graphs; the exact strong isomet-ric dimension for cycles and hypercubes; and the isometric dimension for trees is… (More)

In cellular networks, channels must be assigned to call requests so that interference constraints are respected and bandwidth is minimized. The number of call requests per cell is continually changing, making channel assignment naturally an online problem. We describe two new online channel assignment algorithms for networks based on a regular hexagonal… (More)

We show that the total domination number of a graph G whose complement , G c , does not contain K3;3 is at most (G c), except for complements of complete graphs, and graphs belonging to a certain family which is characterized. In the case where G c does not contain K4;4 we show that there are four exceptional families of graphs, and determine the total… (More)

A method to generate lower bounds for the channel assignment problem is given. The method is based on the reduction of the channel assignment problem to a problem of covering the demand in a cellular network by pre-assigned blocks of cells, called tiles. This tile cover approach is applied to networks with a cosite constraint and two different constraints… (More)

In this short note, we supply a new upper bound on the cop number in terms of tree de-compositions. Our results in some cases extend a previously derived bound on the cop number using treewidth.