In this talk we will discuss some examples of graph homomorphisms. More precisely, the graph parameters which can be represented by counting the graph homomorphisms. The main reference is Section 2 in [2].

For a graph G, let     max : is an edge cut of b G D D G  . For graphs G and H, a map     :V G V H   is a graph homomorphism if for each   e uv E G   ,       u v E H    . In 1979, Erdös proved by probabilistic methods that for p ≥ 2 with

A graph homomorphism is a vertex map which carries edges from a source graph to edgesin a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem(MAX H -COL) are edge-weighted graphs G and the objective is to find a subgraph of G that hasmaximal total edge weight, under the condition that the subgraph has a homomorphism to H ;note that for H = Kk th...

Galois comodules over a coring can be characterised by properties of the relative injective comodules. They motivated the definition of Galois functors over some comonad (or monad) on any category and in the first section of the present paper we investigate the role of the relative injectives (projectives) in this context. Then we generalise the notion of corings (derived from an entwining of a...

Following the last talk on graph homomorphisms, we continue to discuss some examples of graph homomorphisms. But this time we will focus on some models, that is, the homomorphism G → H for the graph H with fixed weights. The main reference is Section 1 in [2].

We show that if a graph H is k-colorable, then (k−1)-branching walks on H exhibit long range action, in the sense that the position of a token at time 0 constrains the configuration of its descendents arbitrarily far into the future. This long range action property is one of several investigated herein; all are similar in some respects to chromatic number but based on viewing H as the range, in...

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...