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Homomorphisms of graphs and their global maps [chapter]

Masakazu Nasu
1981 Lecture Notes in Computer Science  
and onto global maps of homomorphisms of graphs.  ...  We can characterize homomorphisms between strongly connected graphs with one-to-one and onto global maps in terms of definiteness of their induced regular and b-regular homomorphisms. Theorem 8.  ... 
doi:10.1007/3-540-10704-5_14 fatcat:wjsgdwtb5zghnn646wty2qv4ou

Cantor–Bernstein type theorem for locally constrained graph homomorphisms

Jiří Fiala, Jana Maxová
2006 European journal of combinatorics (Print)  
We show that the simultaneous existence of a single locally surjective graph homomorphism between a graph G and a connected and finite graph H together with some locally injective homomorphism between  ...  the same pair of graphs assures that both homomorphisms are locally bijective.  ...  For graphs G and H a (graph) homomorphism is a vertex mapping f : V G → V H satisfying the property that ( f (u), f (v)) is an edge of H whenever vertices u and v are adjacent in G.  ... 
doi:10.1016/j.ejc.2006.06.003 fatcat:sducpzmqd5c5fdraxnur6zu2tq

Homomorphisms of Multisource Trees into Networks with Applications to Metabolic Pathways

Qiong Cheng, Robert Harrison, Alexander Zelikovsky
2007 2007 IEEE 7th International Symposium on BioInformatics and BioEngineering  
We have performed pairwise mapping of all pathways for four organisms (E. coli, S. cerevisiae, B. subtilis and T. thermophilus species) and found a reasonably large set of statistically significant pathway  ...  Network mapping is a convenient tool for comparing and exploring biological networks; it can be used for predicting unknown pathways, fast and meaningful searching of databases, and potentially establishing  ...  Acknowledgments We thank Professor Pinter and Oleg Rokhlenko for giving access to their software package MetaPathwayHunter, Professor Karp and Dr.  ... 
doi:10.1109/bibe.2007.4375587 dblp:conf/bibe/ChengHZ07 fatcat:zn667eflfbdo3pch2dqa2wzr4u

Modeling Pointer Redirection as Cyclic Term-graph Rewriting

Dominique Duval, Rachid Echahed, Frédéric Prost
2007 Electronical Notes in Theoretical Computer Science  
We define first the category of graphs we consider and then we define rewrite rules as pairs of graph homomorphisms of the form L ← K → R.  ...  We tackle the problem of data-structure rewriting including global and local pointer redirections.  ...  As in the rest of the paper, this map is simply denoted ϕ, and this is not ambiguous: indeed, if two graph homomorphisms ϕ, ψ : G → H are such that their underlying maps are equal ϕ = ψ : N G → N H , then  ... 
doi:10.1016/j.entcs.2006.10.027 fatcat:jdx7tbgrubfolpbnuetw7kfwqe

Constant-to-one and onto global maps of homomorphisms between strongly connected graphs

Masakazu Nasu
1983 Ergodic Theory and Dynamical Systems  
global map is finite-to-one and onto, and using them we study the structure of constant-toone and onto global maps of homorphisms between strongly connected graphs and that of constant-to-one and onto  ...  The global maps of homomorphisms of directed graphs are very closely related to homomorphisms of a class of symbolic dynamical systems called subshifts of finite type.  ...  ) and hence the global map of a homomorphism of graphs is a homomorphism of subshifts of finite type.  ... 
doi:10.1017/s0143385700002042 fatcat:jb4cnis4h5az5i2hjdpgkse5vu

Knowledge Representation Analysis of Graph Mining [article]

Matthias van der Hallen, Sergey Paramonov, Michael Leuschel, Gerda Janssens
2016 arXiv   pre-print
In short, this problem asks us to find a graph that frequently occurs as a subgraph among a set of example graphs.  ...  In this paper we study the graph mining problem as an example of a higher order problem.  ...  Thus, we are required to promote the homomorphic mapping functions to a global property in the vocabulary, even though we are only interested in the existence of a mapping, and not in the concrete instance  ... 
arXiv:1608.08956v1 fatcat:qhocefipvzhojfy7mhs2wmem6y

Graph and semigroup homomorphisms on networks of relations

Douglas R. White, Karl P. Reitz
1983 Social Networks  
While the local structure of social roles is captured in a bundle homomorphism by putting together points with the same patterns of incoming and outgoing arrows, the global or relational structure of their  ...  To capture the global role structure of multiplex social relationships, we require a stronger homomorphism, one which has properties of both the bundle homomorphism and the regular homomorphism.  ...  Let G = (P, R) be a graph and f: P + P' be an onto map for some set P'. If R' is the relation on P' induced by R and f, and G' = (P', R'), then the map f: G + G' is a full graph homomorphism.  ... 
doi:10.1016/0378-8733(83)90025-4 fatcat:6xf6esikorglpbqscgjf7ztmfq

A remark about actions of lattices on free groups

Martin R. Bridson, Benson Farb
2001 Topology and its Applications  
Every homomorphism from an irreducible, noncocompact lattice in a higher-rank semisimple Lie group to the outer automorphism group of a free group must have a finite image.  ...  In fact all homomorphisms Γ → Out(F n ) arise from actions of Γ on finite graphs. Corollary 2. Let Γ be as above and let ψ : Γ → Out(F n ) be a homomorphism.  ...  Then there is a finite graph G with fundamental group F n and an action of Γ on G by automorphisms such that the induced homomorphism Γ → Out(F n ) is ψ.  ... 
doi:10.1016/s0166-8641(99)00174-1 fatcat:cdukhizu3rfljp2fiavbd3uahm

Vicinity Respecting Homomorphisms for Abstracting System Requirements [chapter]

Jörg Desel, Agathe Merceron
2010 Lecture Notes in Computer Science  
Vicinity respecting homomorphisms are presented as a means to refine and abstract these nets.  ...  ., dependencies between computational elements and they preserve important structural properties of nets, such as S-and T-components, siphons and traps and the free choice property.  ...  They are special graph homomorphisms that are able to formalize abstractions including contractions of graphs not only in their breadth but also in their length.  ... 
doi:10.1007/978-3-642-18222-8_1 fatcat:b4bjasmhzrd73cd5xcxk4i5dcy

Local to global property in free groups [article]

Ofir David
2019 arXiv   pre-print
The local to global property for an equation ψ over a group G asks to show that ψ is solvable in G if and only if it is solvable in every finite quotient of G.  ...  In this paper we focus that in order to prove this local to global property for free groups G=F_k, it is enough to prove for k less or equal the number of parameters in ψ.  ...  Consider the map Γ S → Γ N . The image of this map is a sub Stallings graph of Γ N corresponding to some Γ H for some H ≤ N .  ... 
arXiv:1907.05968v2 fatcat:lwbrqsgfdjdzxjdfku3xjhnm6m

Subgraph Frequencies: Mapping the Empirical and Extremal Geography of Large Graph Collections [article]

Johan Ugander, Lars Backstrom, Jon Kleinberg
2013 arXiv   pre-print
In this work, we draw on the theory of graph homomorphisms to formulate and analyze such a representation, based on computing the frequencies of small induced subgraphs within each graph.  ...  Together, these two complementary frameworks shed light on a fundamental question pertaining to social graphs: what properties of social graphs are 'social' properties and what properties are 'graph' properties  ...  This work was supported in part by NSF grants IIS-0910664 and IIS-1016099.  ... 
arXiv:1304.1548v2 fatcat:entafhr45nhkvp7dtup6gjh2iy

Subgraph frequencies

Johan Ugander, Lars Backstrom, Jon Kleinberg
2013 Proceedings of the 22nd international conference on World Wide Web - WWW '13  
In this work, we draw on the theory of graph homomorphisms to formulate and analyze such a representation, based on computing the frequencies of small induced subgraphs within each graph.  ...  Together, these two complementary frameworks shed light on a fundamental question pertaining to social graphs: what properties of social graphs are 'social' properties and what properties are 'graph' properties  ...  This work was supported in part by NSF grants IIS-0910664 and IIS-1016099.  ... 
doi:10.1145/2488388.2488502 dblp:conf/www/UganderBK13 fatcat:rjtmmwlqdbac7e23vh2xv3g6hm

Locally constrained graph homomorphisms—structure, complexity, and applications

Jiří Fiala, Jan Kratochvíl
2008 Computer Science Review  
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  ...  Graph homomorphisms are mappings between sets of vertices of two graphs having the following property: If two vertices form an edge of the source graph then their images form an edge in the target graph  ... 
doi:10.1016/j.cosrev.2008.06.001 fatcat:p57dezmpfjhzpf5xahy4f7rtga

Graph theory and algorithms

1982 Discrete Mathematics  
N .S~tfho~ou~~~ : The complexity of path problems in graphs and path systems of bounded bandwidth. M.-J. Kreowski: A compqrisort between petri-nets and graph gammars. W.  ...  Reisig: A graph grammar rt presentation of nonsequential processes. J. Perl/J. Ebert: Reachability Homomorphisms on nets. B. Mahr: A bird's_eye view to path problems. P.  ...  Nasu: Homomorphisms of heir global maps. T. ashiwabara: Algorithms for some intersection graphs. T. Asano, &u&i rann N.  ... 
doi:10.1016/0012-365x(82)90093-0 fatcat:xuedghfhonhylm7uqbmgleu3qi

Page 3788 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
Author’s summary: “L homomorphisms, i.e., structure-preserving mappings between OL systems, are introduced.  ...  between synchronous and asynchronous cellular spaces, from the point of view of the equivalence of their respective array transformations with reference to a certain alphabet.  ... 
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