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Countable homogeneous multipartite graphs

Tristan Jenkinson, J.K. Truss, Daniel Seidel
2012 European journal of combinatorics (Print)  
We give a classification of all the countable homogeneous multipartite graphs. This generalizes the similar result for bipartite graphs given in [5] .  ...  In terms of coding graphs, the main results given are that any coding graph represents a unique countable homogeneous multipartite graph, and that any countable homogeneous multipartite graph is represented  ...  Introduction In this paper we describe the classification of all the countable homogeneous multipartite graphs.  ... 
doi:10.1016/j.ejc.2011.04.004 fatcat:o6tyiyvfmbfdlfp7dzv5rwoeiq

Countable connected-homogeneous graphs

R. Gray, D. Macpherson
2010 Journal of combinatorial theory. Series B (Print)  
of countably many copies of a finite connected-homogeneous graph.  ...  In this paper we classify the countably infinite connected-homogeneous graphs.  ...  Let Γ be a countable connected C -homogeneous graph. If the neighbourhood of a vertex of Γ is isomorphic to the random, co-K n -free, K n -free, or complete multipartite graph, then Γ is homogeneous.  ... 
doi:10.1016/j.jctb.2009.04.002 fatcat:unuaac5ywzeazdmf32cd3yqwjy

Page 37 of Mathematical Reviews Vol. , Issue 86a [page]

1986 Mathematical Reviews  
—n—1,n) it is always the case that 1(K(n1,n2,---,n,)) = 1(K(n1,n2)), and in the two exceptional cases, for r sufficiently large, the interval number of the multipartite graph exceeds that of the bipartite  ...  Corominas, On better quasi-ordering countable trees (pp. 35-53); Richa’a Dean, A con- struction for large families of k-element sets having the Erdés in- tersection property (pp. 55-56); J.-P.  ... 

Permutation monoids and MB-homogeneity for graphs and relational structures [article]

Thomas D. H. Coleman, David M. Evans, Robert D. Gray
2019 arXiv   pre-print
We also consider MB-homogeneity for various well-known examples of homogeneous structures and in particular give a complete classification of countable homogeneous undirected graphs that are also MB-homogeneous  ...  graphs.  ...  Recall that the random graph R is the countable universal homogeneous graph.  ... 
arXiv:1802.04166v2 fatcat:5tj67zxhvre7hlifnrsxgaevty

Homogeneous coloured multipartite graphs

Deborah C. Lockett, John K. Truss
2014 European journal of combinatorics (Print)  
We classify the countable homogeneous coloured multipartite graphs with any finite number of parts.  ...  By Fraisse's Theorem this amounts to classifying the families F of pairwise non-embeddable finite coloured multipartite graphs for which the class Forb(F) of multipartite graphs which forbid these is an  ...  is realized or omitted in a given homogeneous multipartite graph.  ... 
doi:10.1016/j.ejc.2014.06.006 fatcat:t2bbygfv6fbr5koupegs7g7xhq

Connected-homomorphism-homogeneous graphs [article]

Deborah Lockett
2012 arXiv   pre-print
The finite C-II (connected-homogeneous) graphs were classified by Gardiner in 1976, and from this we obtain classifications of the finite C-HI and C-MI finite graphs.  ...  Specifically, we study the classes of finite connected-homomorphism-homogeneous graphs, with the aim of producing classifications.  ...  of countable C-homogeneous graphs [10] .  ... 
arXiv:1207.4373v1 fatcat:lj5cidsn25eflm7jzumqllnyku

Homogeneity and related topics: An extended bibliography [article]

Gregory Cherlin
2021 arXiv   pre-print
We give a bibliography of works relating to homogeneous structures in the sense of Fra\"iss\'e, and related topics, mainly through 2016, with some narrow updating through 2021.  ...  Enomoto [1981] , Gardiner [1976c] , [1978b] ; partitioned graphs: Rose [2011] ; multipartite edge-colored graphs: Jenkinson, Seidel, and Truss [2012] , Lockett and Truss [2014a] ; 3-edge colored  ...  Some of this bears on the classification of countable homogeneous structures of various types or the close study of their automorphism groups and associated combinatorial problems.  ... 
arXiv:2111.15429v2 fatcat:di6lzukkvzdwlcvabb7lozrdha

Forthcoming papers

1991 Discrete Mathematics  
We show that (n, m)+ (n -1, m -4) for all m s [ the following problem is solved: Let G be a multipartite graph with a given partition of its vertex set, A, U A, U . . . U A,.  ...  In particular, if S is homogeneous, the divisibility or indivisibility of age S is related to the way in which the elements of age S amalgamate.  ... 
doi:10.1016/0012-365x(91)90063-8 fatcat:yv6fsd3i3rgl3ccthj5vwdfhvy

Homogeneous and Ultrahomogeneous Linear Spaces

Alice Devillers, Jean Doyen
1998 Journal of combinatorial theory. Series A  
We give a complete classification of all homogeneous (resp. ultrahomogeneous) linear spaces, without making any finiteness assumption on the number of points of S.  ...  A linear space S is homogeneous if, whenever the linear structures induced on two finite subsets S$ and S" are isomorphic, there is at least one automorphism of S mapping S$ onto S".  ...  Gardiner [7] proved that a finite ultrahomogeneous undirected graph is either a disjoint union of isomorphic complete graphs or a regular complete multipartite graph or the 3_3 lattice graph or the graph  ... 
doi:10.1006/jcta.1998.2887 fatcat:tsenlwojunhwfm3oztmxpig35i

Page 44 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
A graph G is locally homogeneous if the neighbourhood of every vertex induces the same graph; if this graph is H then G is also called a locally H graph.  ...  First, it follows from work of Brouwer, Cohen and Neumaier (or in a slightly weaker form from the work of Soltés) that for regular graphs H any connected locally H graph is complete multipartite, provided  ... 

Countable homogeneous linearly ordered posets

Igor Dolinka, Dragan Mašulović
2012 European journal of combinatorics (Print)  
We characterise all countable homogeneous linearly ordered posets, thus extending earlier work by Cameron on countable homogeneous permutations.  ...  As a consequence of our main result it turns out that, up to isomorphism, there is a unique homogeneous linear extension of the random poset, the unique countable homogeneous universal partially ordered  ...  13] , countable tournaments [12] , countable digraphs [2] , finite groups [3] , countable permutations [1] , and countable multipartite graphs [9] .  ... 
doi:10.1016/j.ejc.2012.06.006 fatcat:edgwsymivvc3torxowim4gaaim

Finite 3-connected homogeneous graphs [article]

Cai Heng Li, Jin-Xin Zhou
2018 arXiv   pre-print
In 1985, Cameron and Macpherson determined all finite (G, 3)-homogeneous graphs. In this paper, we develop a method for characterising (G,3)-connected homogeneous graphs.  ...  It is shown that for a finite (G,3)-connected homogeneous graph =(V, E), either G_v^(v) is 2--transitive or G_v^(v) is of rank 3 and has girth 3, and that the class of finite (G,3)-connected homogeneous  ...  First, we provide a family of locally connected graphs.  ... 
arXiv:1810.01535v2 fatcat:xpe65toagrezboo4ueuowxo5mq

Amenability and unique ergodicity of automorphism groups of countable homogeneous directed graphs [article]

Micheal Pawliuk, Miodrag Sokic
2017 arXiv   pre-print
We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics.  ...  The starting point in all cases is the determination of the universal minimal flow for the automorphism group, which in the context of countable homogeneous directed graphs is given in [10] and the papers  ...  Ramsey expansions of countable homogeneous directed graphs We now introduce the directed graphs that appear in Cherlin's classification.  ... 
arXiv:1712.09461v1 fatcat:cu3eq6kxuncatip7qdcfgynrii

Complexities of relational structures [article]

David Hartman, Jan Hubicka, Jaroslav Nesetril
2013 arXiv   pre-print
graph K r , (2) complete multipartite graph (complement of (1)), (3) a 5-cycle, and (4) a line graph L(K 3,3 ) of the complete bipartite graph K 3,3 .  ...  Age of B 2 is the class of all finite bipartite graphs. Every countable bipartite graph can be found as an induced subgraph of B 2 (it is an universal bipartite graph).  ...  The complexity of an ω-categorical graph universal for Forb h (F Cn ), n ≥ 5, (of graphs without odd cycles of length at most n) is at least 2.  ... 
arXiv:1309.4266v1 fatcat:57dxzpd4gbclhcktyks665shoa

Homomorphism-homogeneous L-colored graphs [article]

David Hartman, Jan Hubicka, Dragan Masulovic
2012 arXiv   pre-print
A full classification of finite MH-homogeneous L-colored graphs where L is a chain is provided, and we show that the classes MH and HH coincide.  ...  In this paper we consider L-colored graphs, that is, undirected graphs without loops where sets of colors selected from L are assigned to vertices and edges.  ...  He has shown that a finite graph is ultrahomogeneous if and only if it is isomorphic to one of the following graphs: 1. a disjoint union of complete graphs all of the same size, k i=1 K n , 2. multipartite  ... 
arXiv:1204.5879v1 fatcat:ds2ucyhmg5dzhord47zju4yupa
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