For graphs G and H , a homomorphism from G to H is a function φ : V (G) → V (H), which maps vertices adjacent in G to adjacent vertices of H . A homomorphism is locally injective if no two vertices with a common neighbor are mapped to a single vertex in H . Many cases of graph homomorphism and locally injective graph homomorphism are NPcomplete, so there is little hope to design polynomial-time...

We show that for every binary matroid $N$ there is a graph $H_*$ such the graphic $M_G$ of $G$, matroid-homomorphism from to if and only graph-homomorphism $G$ $H_*$. With this we prove complexity dichotomy problem $\rm{Hom}_\mathbb{M}(N)$ deciding $M$ admits homomorphism $N$. The polynomial time solvable has loop or no circuits odd length, otherwise $\rm{NP}$-complete. also get dichotomies lis...

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

We consider the complexity of oriented homomorphism and two of its variants, namely strong oriented homomorphism and pushable homomorphism, for planar graphs with large girth. In each case, we consider the smallest target graph such that the corresponding homomorphism is NP-complete. These target graphs T4, T5, and T6 have 4, 5, and 6 vertices, respectively. For i ∈ {4, 5, 6} and for every g, w...

For every pair of nite connected graphs F and H, and every integer k, we construct a universal graph U with the following properties: 1. There is a homomorphism : U ! H, but no homomorphism from F to U . 2. For every graph G with maximal degree no more than k having a homomorphism h : G! H, but no homomorphism from F to G, there is a homomorphism : G! U , such that h = . Particularly, this solv...

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...