Lower bounds on mt(r, s)

Lower bounds on the signed (total) $k$-domination number

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

Lower bounds on kernelization

Preprocessing (data reduction or kernelization) to reduce instance size is one of the most commonly deployed heuristics in the implementation practice to tackle computationally hard problems. However, a systematic theoretical study of them remained elusive so far. One of the reasons for this is that if an input to an NP -hard problem can be processed in polynomial time to an equivalent one of s...

Two lower bounds on

The lower bounds on communication complexity measures of language generation by Parallel Communicating Grammar Systems (PCGS) are investigated. The rst result shows that there exists a language that can be generated by some dag-PCGS (PCGS with communication structures realizable by directed acyclic graphs) consisting of 3 grammars, but by no PCGS with tree communication structure. The second re...

Lower bounds on treespan

Recently Fomin, Heggernes and Telle [Algorithmica 41 (2004) 73] introduced the notion of the treespan of a graph as a natural extension of the well-known bandwidth. They motivate this new concept from different viewpoints involving graph searching, tree decompositions and elimination orderings. In the present paper we prove several lower bounds on the treespan.  2005 Published by Elsevier B.V.

Some Lower Bounds for Estrada Index