We study online partitioning of posets from a graph theoretical point of view, which is coloring and cocoloring in comparability graphs. For the coloring problem, we analyse the First-Fit algorithm and show a ratio of O( √ n); furthermore, we devise an algorithm with a competitivity ratio of χ+1 2 . For the cocoloring problem, we point out a tight bound of n 4 + 1 2 and we give better bounds in...

Given two nonnegative integers h and k, an L(h, k)-labeling of a graph G = (V, E) is a map from V to a set of integer labels such that adjacent vertices receive labels at least h apart, while vertices at distance at most 2 receive labels at least k apart. The goal of the L(h, k)-labeling problem is to produce a legal labeling that minimizes the largest label used. Since the decision version of ...

We introduce a new graph width parameter, called special induced matching width, shortly sim-width, which does not increase when taking induced minors. For a vertex partition (A,B) of a graphG, this parameter is based on the maximum size of an induced matching {a1b1, . . . , ambm} in G where a1, . . . , am ∈ A and b1, . . . , bm ∈ B. Classes of graphs of bounded sim-width are much wider than cl...

In 2013 Belmonte and Vatshelle used mim-width, a graph parameter bounded on interval graphs and permutation graphs that strictly generalizes clique-width, to explain existing algorithms for many domination-type problems, also known as (σ, ρ)problems or LC-VSVP problems, on many special graph classes. In this paper, we focus on chordal graphs and co-comparability graphs, that strictly contain in...

Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear extensions of these posets. We want to know which choice of orientation maximizes the number of linear extensions of the corresponding poset, and this problem w...

‎in this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎we also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

We consider geometric and graph-theoretic aspects of the well-known paradigm \killing two birds with one stone". Consider that we have a set X of n-points in space and a compact plane convex set S. We deene a graph G(X; S), called the ray shooting graph, on X as follows: The points of X are the vertices and fpi; pj g, pi; pj 2 X , is an edge if and only if the line joining pi to pj intersects S...

Finding graph indices which are unbiased to network size is of high importance both within a given field and across fields for enhancing the comparability over the cornucopia of modern network science studies as well as in subnetwork comparisons of the same network. The degree variance is an important metric for characterising graph heterogeneity and hub dominance, however this clearly depends ...

It is well known that every 2-edge-connected graph can be oriented so that the resulting digraph is strongly connected. Here we study the problem of orienting a connected graph with cut edges in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y. After transforming this problem, we prove a key theorem about the transformed problem that allo...