Complexity of Locally Injective Homomorphism to the Theta Graphs
نویسندگان
چکیده
A Theta graph is a multigraph which is a union of at least three internally disjoint paths that have the same two distinct end vertices. We show full computational complexity characterization of the problem of deciding the existence of a locally injective homomorphism from an input graph G to any fixed Theta graph.
منابع مشابه
Complexity of locally-injective homomorphisms to tournaments
Given two graphs G = (VG, EG) and H = (VH , EH), a homomorphism from G to H is a function f : VG → VH such that for every uv ∈ EG, f(u)f(v) ∈ EH . A homomorphism from G to H is referred to as an H-colouring of G and the vertices of H are regarded as colours. The graph H is called the target of the homomorphism. These definitions extend to directed graphs by requiring that the mapping must prese...
متن کاملExact Algorithm for Graph Homomorphism and Locally Injective Graph Homomorphism
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...
متن کاملLocally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree
A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether a given graph G allows a homomorphism to a given graph H that is locally bijective, surjective, or injective, respectively, are NP-complete, even w...
متن کاملLocally Injective Homomorphism to the Simple Weight Graphs
A Weight graph is a connected (multi)graph with two vertices u and v of degree at least three and other vertices of degree two. Moreover, if any of these two vertices is removed, the remaining graph contains a cycle. A Weight graph is called simple if the degree of u and v is three. We show full computational complexity characterization of the problem of deciding the existence of a locally inje...
متن کاملLocally constrained graph homomorphisms - structure, complexity, and applications
A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...
متن کامل