In a fractional coloring, vertices of a graph are assigned measurable subsets of the real line
and adjacent vertices receive disjoint subsets; the fractional chromatic number of a graph is …

We prove that if G is a graph and f (v)≤ 1/(d (v)+ 1/2) for each v∈ V (G), then either G has an
independent set of size at least∑ v∈ V (G) f (v) or G contains a clique K such that∑ v∈ K f …

The famous lower bound α (G)≥∑ u∈ V (G) 1 d G (u)+ 1 on the independence number α
(G) of a graph G due to Caro and Wei is known to be satisfied with equality if and only if the …

Many of the most celebrated and influential results in graph coloring, such as Brooks'
Theorem and Vizing's Theorem, relate a graph's chromatic number to its clique number or …

We propose new bounds on the domination number and on the independence number of a
graph and show that our bounds compare favorably to recent ones. Our bounds are …

We propose new bounds on the domination number and on the independence number of a
graph and show that our bounds compare favorably to recent ones. Our bounds are …