Graphs with disjoint cycles classification via the talented monoid
نویسندگان
چکیده
We characterise directed graphs consisting of disjoint cycles via their talented monoids. show that a graph E consists precisely when its monoid TE has certain Jordan-Hölder composition series. These are whose associated Leavitt path algebras Lk(E) have finite Gelfand-Kirillov dimension (GKdim). this can be determined as the length ideal series monoid. Since is positive cone graded Grothendieck group K0gr(Lk(E)), we conclude for and F, if K0gr(Lk(E))≅K0gr(Lk(F)) then GKdimLk(E)=GKdimLk(F), thus providing more evidence Graded Classification Conjecture algebras.
منابع مشابه
Random Graphs with Few Disjoint Cycles
The classical Erdős-Pósa theorem states that for each positive integer k there is an f(k) such that, in each graph G which does not have k + 1 disjoint cycles, there is a blocker of size at most f(k); that is, a set B of at most f(k) vertices such that G − B has no cycles. We show that, amongst all such graphs on vertex set {1, . . . , n}, all but an exponentially small proportion have a blocke...
متن کاملDisjoint Cycles and Chorded Cycles in Graphs
Very recently, Bialostocki et al. proposed the following conjecture. Let r, s be two nonnegative integers and let G = (V (G), E(G)) be a graph with |V (G)| ≥ 3r + 4s and minimum degree δ(G) ≥ 2r + 3s. Then G contains a collection of r cycles and s chorded cycles, all vertex-disjoint. We prove that this conjecture is true.
متن کاملGraphs with many Vertex-Disjoint Cycles
We consider finite and undirected graphs G with vertex set V (G) and edge set E(G) that may contain multiple edges but no loops. We use standard terminology [15] and only recall a few notions. If an edge e ∈ E(G) is incident with the two vertices u and v in V (G), then we write e = uv. The neighbourhood NG(u) of a vertex u ∈ V (G) is the set of vertices v ∈ V (G) with e = uv for some e ∈ E(G). ...
متن کاملDisjoint Hamiltonian cycles in graphs
Let G be a 2(k + I)-connected graph of order n. It is proved that if uv rJ. E(G) implies that max{d(u), d(v)} ?: ~ + 2k then G contains k + 1 pairwise disjoint Hamiltonian cycles when c5 (G) ?: 4k + 3. 1 .. Introduction All graphs we consider are finite and simple. We use standard terminology and notation from Bondy and Murty [2] except as indicated. Let G = (V(G), E(G)) be a graph with vertex ...
متن کاملDisjoint chorded cycles in graphs
We propose the following conjecture to generalize results of Pósa and Corrádi Hajnal. Let r, s be nonnegative integers and let G be a graph with |V (G)| ≥ 3r + 4s and minimal degree δ(G) ≥ 2r + 3s. Then G contains a collection of r + s vertex disjoint cycles, s of them with a chord. We prove the conjecture for r = 0, s = 2 and for s = 1. The corresponding extremal problem, to find the minimum n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2021.11.022