We describe combinatorial games on graphs in which two players antagonistically build a representation of a subgraph of a given graph. We show that for a large class of these games, determining whether a given instance is a winning position for the next player is PSPACE-hard. In contrast, we give polynomial time algorithms for solving some versions of the games on trees.

Clique-width is an important graph parameter whose computation is NP-hard. In fact we do not know of any other algorithm than brute force for the exact computation of clique-width on any non-trivial graph class. Results so far indicate that proper interval graphs constitute the first interesting graph class on which we might have hope to compute clique-width, or at least its linear variant line...

The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...

Here we give some insight for our definition of the family of graph difference operators (5) and (6), based on the idea of piecewise polynomials over graphs. In the univariate case, sparsity of β under the difference operator D implies a specific kth order piecewise polynomial structure for the components of β [6, 8]. Since the components of β correspond to (real-valued) input locations x = (x1...

In this note we improve our upper bound given in [7] by showing that every 9-fold covering of a point set in R by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering that does not decompose into two coverings. We also prove that certain dynamic interval coloring problems are equivalent to the above question. The same b...

for a graph $g$ let $gamma (g)$ be its domination number. we define a graph g to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ed}$ graph) if $g$ has no efficient dominating set (eds) but every graph formed by removing a single vertex from $g$ has at least one eds, and (ii) a hypo-unique domination graph (a hypo-$mathcal{ud}$ graph) if $g$ has at least two minimum dominating sets...

A graph G is an interval graph if there is a one-one correspondence between its vertices and a family I of intervals, such that two vertices in G are adjacent if and only if their corresponding intervals overlap. In this context, the family I of intervals is referred to as an interval model of G. Recently, a powerful architecture called the reconngurable mesh has been proposed: in essence, a re...

We present scalable coarse grained parallel algorithms for solving interval graph problems on a BSP-like model{Coarse Grained Multicomputers (CGM). The problems we consider include: nding maximum independent set, maximum weighted clique, minimum coloring and cut vertices and bridges. With scalability at n p p ; 8 > 0 (here n denotes the total input size and p the number of processors), our algo...