In this paper, we use the concept of edge-colored graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirement...
A graph G = (V, E) is called (k, k )-total weight choosable if the following holds: For any total list assignment L which assigns to each vertex x a set L(x) of k real numbers, an...
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
In graphical modelling, a bi-directed graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bi...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...