Let G be a simple graph and let us color its edges so that the multisets of colors around each vertex are distinct. The smallest number of colors for which such a coloring exists is called the irregular coloring number of G and is denoted by c(G). We determine the exact value of the irregular […]

Section:
Graph and Algorithms

We show that for a planar graph with no g-grid minor there exists a tree-decomposition of width at most 5g - 6. The proof is constructive and simple. The underlying algorithm for the tree-decomposition runs in O(n(2) log n) time.

Section:
Graph and Algorithms

For each integer partition mu, let e (F) over tilde (mu)(q; t) be the coefficient of x(1) ... x(n) in the modified Macdonald polynomial (H) over tilde (mu). The polynomial (F) over tilde (mu)(q; t) can be regarded as the Hilbert series of a certain doubly-graded S(n)-module M(mu), or as a q, […]

Section:
Combinatorics

In this work we investigate the algorithmic complexity of computing a minimum C(k)-transversal, i.e., a subset of vertices that intersects all the chordless cycles with k vertices of the input graph, for a fixed k \textgreater= 3. For graphs of maximum degree at most three, we prove that this […]

Section:
Graph and Algorithms

De Bruijn and Erdos proved that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvatal suggested a possible generalization of this theorem in the framework of metric spaces. We provide partial results in this direction.

Section:
Combinatorics

We study expansions in non-integer negative base -beta introduced by Ito and Sadahiro. Using countable automata associated with (-beta)-expansions, we characterize the case where the (-beta)-shift is a system of finite type. We prove that, if beta is a Pisot number, then the (-beta)-shift is a sofic […]

Section:
Automata, Logic and Semantics

Monitoring physical phenomena in Sensor Networks requires guaranteeing permanent communication between nodes. Moreover, in an effective implementation of such infrastructure, the delay between any two consecutive communications should be minimized. The problem is challenging because, in a restricted […]

Section:
Distributed Computing and Networking