منابع مشابه
Amalgams and χ-Boundedness
A class of graphs is hereditary if it is closed under isomorphism and induced subgraphs. A class G of graphs is χ-bounded if there exists a function f : N → N such that for all graphs G ∈ G, and all induced subgraphs H of G, we have that χ(H) ≤ f(ω(H)). We prove that proper homogeneous sets, clique-cutsets, and amalgams together preserve χ-boundedness. More precisely, we show that if G and G∗ a...
متن کاملSubstitution and χ-boundedness
A class G of graphs is said to be χ-bounded if there is a function f : N → R such that for all G ∈ G and all induced subgraphs H of G, χ(H) ≤ f(ω(H)). In this paper, we show that if G is a χ-bounded class, then so is the closure of G under any one of the following three operations: substitution, gluing along a clique, and gluing along a bounded number of vertices. Furthermore, if G is χ-bounded...
متن کاملQuasiconvexity and Amalgams
We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that is such that all their finitely generated subgroups are quasiconvex. It is known that free groups, hyperbolic surface groups and most 3-dimensional Kleinian...
متن کاملAmalgams and the Coset Graph
Informally, an amalgam is a group ‘sitting inside’ two other groups and the coset graph is a way to look at how the cosets of subgroups interact. These are combined in the amalgam method — a way of classifying amalgams satisfying certain conditions. The amalgam method was used in the classifications of finite simple groups, and is discussed in Classification of Finite Simple Groups no. 2 by Gor...
متن کاملAMALGAMS OF L ' AND l
(i.i) ll/IU=( t \ n » — oo makes (L9 l ) into a Banach space. The idea of considering the amalgam (L, l\ as opposed to the Lebesgue space L = (L,l), is a natural one because it allows us to separate the global behavior from the local behavior of a function. This idea goes back to 1926 and Norbert Wiener who considered the special cases (L,1) and (L, l°°) in [Wl] and (L°°, I) and (L\ l°°) in [W2...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2016
ISSN: 0364-9024
DOI: 10.1002/jgt.22012