Albertson and Berman conjectured that every planar graph has an induced forest on half of its vertices. The best known lower bound, due to Borodin, is that every planar graph has an induced forest on two fifths of its vertices. In a related result, Chartran and Kronk, proved that the vertices of every planar graph can be partitioned into three sets, each of which induce a forest. We show tighte...

Albertson and Berman [1] conjectured that every planar graph has an induced forest on half of its vertices; the current best result, due to Borodin [3], is an induced forest on two fifths of the vertices. We show that the Albertson-Berman conjecture holds, and is tight, for planar graphs of treewidth 3 (and, in fact, for any graph of treewidth at most 3). We also improve on Borodin’s bound for ...

Let G be a graph embedded on a surface Sε with Euler genus ε > 0, and let P ⊂ V (G) be a set of vertices mutually at distance at least 4 apart. Suppose all vertices of G have H(ε)-lists and the vertices of P are precolored, where H(ε) = ⌊ 7+ √ 24ε+1 2 ⌋ is the Heawood number. We show that the coloring of P extends to a list-coloring of G and that the distance bound of 4 is best possible. Our re...

A simple graph G is said to be regular if its vertices have the same number of neighbors. Otherwise, id="M2"> nonregular. So far, various formulas, such as Albertson index, total and degree deviation, been introduced quantify irregularity a graph. In this paper, we present sharp lower bounds for these indices in terms or...

Rennie on “A mechanistic model linking insect (Hydropsychidae) silk nets to incipient sediment motion in gravel-bedded streams” Lindsey K. Albertson, Leonard S. Sklar, and Bradley J. Cardinale Stroud Water Research Center, Avondale, Pennsylvania, USA, Earth and Climate Sciences, San Francisco State University, San Francisco, California, USA, School of Natural Resources and Environment, Universi...

We use graph homomorphisms and the chromatic properties of the Petersen graph to prove some inequalities on systems of sets. These inequalities are then used to find counterexamples to a conjecture of Albertson and Collins on the monotonicity of the chromatic difference sequence of a vertex-transitive graph.

Received Let G = (V; E) be a graph with n vertices, chromatic number (G) and list chromatic number`(G): Suppose each vertex of V (G) is assigned a list of t colors. Albertson, Grossman and Haas 1] conjectured that at least t ` (G) n vertices can be colored properly from these lists. Albertson et. al. 1] and Chappell 3] proved partial results concerning this conjecture. This paper presents algor...

En esta reseña, se delinean los componentes centrales de la obra Contornos lo político. Ensayos Sociológicos sobre memoria, protesta, violencia y Estado, del profesor Marco Estrada. También reflexiona unidad temática conceptual libro, algunas preguntas que deja pendientes, sociología pública enarbolada por el autor. El argumento principal afirma que, a pesar diversidad sus objetos estudio, Estr...

This article presents a randomized matrix-free method for approximating the trace of f(A), where A is large symmetric matrix and f function analytic in closed interval containing eigenvalues A. Our uses combination stochastic estimation (i.e., Hutchinson's method), Chebyshev approximation, multilevel Monte Carlo techniques. We establish general bounds on approximation error this by extending an...