A quasi-line graph is a graph in which the neighbourhood of any vertex can be covered by two cliques; every line graph is a quasi-line graph. Reed conjectured that for any graph G, χ(G) ≤ d12(∆(G) + 1 + ω(G))e [13]. We prove that the conjecture holds if G is a quasi-line graph, extending a result of King, Reed and Vetta, who proved the conjecture for line graphs [8], and improving the bound of ...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

Na-CO2 batteries using earth-abundant Na and greenhouse gas CO2 are promising tools for mobile and stationary energy storage, but they still pose safety risks from leakage of liquid electrolyte and instability of the Na metal anode. These issues result in extremely harsh operating conditions of Na-CO2 batteries and increase the difficulty of scaling up this technology. We report the development...

This paper studies the homomorphism of rings of continuous functions ρ:C(X) → C(Y ), Y a subspace of a Tychonoff space X, induced by restriction. We ask when ρ is an epimorphism in the categorical sense. There are several appropriate categories: we look at CR, all commutative rings, and R/N, all reduced commutative rings. When X is first countable and perfectly normal (e.g., a metric space), ρ ...

We give a complete characterization of all indecomposable involutive solutions the Yang-Baxter equation multipermutation level 2. In first step we present construction some family such and in second prove that every solution with 2 is homomorphic image previously constructed. Analyzing this epimorphism, are able to obtain up isomorphism enumerate these small sizes.