We provide a new constant factor approximation algorithm for the (connected) distance-r dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as planar graphs and graphs with excluded (topological) minors, and notably, these classes form the most general subgraph closed classes of graphs for which a sequent...

We improve the running time of the general algorithmic technique known as Baker’s approach (1994) on H-minor-free graphs from O(n) to O(f(|H |)n) showing that it is fixed-parameter tractable w.r.t. the parameter |H |. The numerous applications include e.g. a 2-approximation for coloring and PTASes for various problems such as dominating set and max-cut, where we obtain similar improvements. On ...

Planar graphs are known to allow subexponential algorithms running in time 2O( √ n) or 2O( √ n logn) for most of the paradigmatic problems, while the brute-force time 2Θ(n) is very likely to be asymptotically best on general graphs. Intrigued by an algorithm packing curves in 2O(n logn) by Fox and Pach [SODA’11], we investigate which problems have subexponential algorithms on the intersection g...

Boolean-width is a recently introduced graph width parameter. If a boolean decomposition of width w is given, several NP-complete problems, such as Maximum Weight Independent Set, k-Coloring and Minimum Weight Dominating Set are solvable in O∗(2O(w)) time [5]. In this paper we study graph classes for which we can compute a decomposition of logarithmic boolean-width in polynomial time. Since 2 =...


 We survey work on coloring, list and painting squares of graphs; in particular, we consider strong edge-coloring. focus primarily planar graphs other sparse classes graphs.

‎For any integer $kgeq 1$‎, ‎a set $S$ of vertices in a graph $G=(V,E)$ is a $k$-‎tuple total dominating set of $G$ if any vertex‎ ‎of $G$ is adjacent to at least $k$ vertices in $S$‎, ‎and any vertex‎ ‎of $V-S$ is adjacent to at least $k$ vertices in $V-S$‎. ‎The minimum number of vertices of such a set‎ ‎in $G$ we call the $k$-tuple total restrained domination number of $G$‎. ‎The maximum num...

We make an attempt to understand the dominating set counting problem in graph classes from the viewpoint of polynomial-time computability. We give polynomial-time algorithms to count the number of dominating sets (and minimum dominating sets) in interval graphs and trapezoid graphs. They are based on dynamic programming. With the help of dynamic update on a binary tree, we further reduce the ti...

In an ordinary edge-coloring of a graph each color appears at each vertex at most once. An f -coloring is a generalized edge-coloring in which each color appears at each vertex v at most f(v) times where f(v) is a positive integer assigned to v. This paper gives efficient sequential and parallel algorithms to find ordinary edge-colorings and f -colorings for various classes of graphs such as bi...