We exploit the close relationship between circular arc graphs and interval graphs to design efficient approximation algorithms for NP-hard Optimization problems on circular arc graphs. The problems considered here are maximum domatic partition and on-line minimum vertex coloring. We present a heuristic for the domatic partition problem with a performance ratio of 4. For on-line coloring, we con...

Domination theory is a well-established topic in graph theory, as well one of the most active research areas. Interest this area partly explained by its diversity applications to real-world problems, such facility location computer and social networks, monitoring communication, coding algorithm design, among others. In last two decades, functions defined on graphs have attracted attention sever...

A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...

Let G = (V,E) be an undirected graph and let π = {V1, V2, . . . , Vk} be a partition of the vertices V of G into k blocks Vi. From this partition one can construct the following digraph D(π) = (π,E(π)), the vertices of which correspond one-to-one with the k blocks Vi of π, and there is an arc from Vi to Vj if every vertex in Vj is adjacent to at least one vertex in Vi, that is, Vi dominates Vj ...

For any integer $kgeq 1$ and any graph $G=(V,E)$ with minimum degree at least $k-1$‎, ‎we define a‎ ‎function $f:Vrightarrow {0,1,2}$ as a Roman $k$-tuple dominating‎ ‎function on $G$ if for any vertex $v$ with $f(v)=0$ there exist at least‎ ‎$k$ and for any vertex $v$ with $f(v)neq 0$ at least $k-1$ vertices in its neighborhood with $f(w)=2$‎. ‎The minimum weight of a Roman $k$-tuple dominatin...

etant donné le rapport réciproque entre la société et la littérature, et vu la dominance extraordinaire du roman, à l'état actuel, sur les autres expressions littéraires, on ne peut s'empêcher de s'interroger sur la cause et l'origine de la primauté du genre romanesque. certes, le roman ne date pas du xixe siècle; il est l'un des héritages des siècles précédents. néanmoins, son déploiement est ...