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Countable homogeneous multipartite graphs

2012
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European journal of combinatorics (Print)
*

We give a classification of all the

doi:10.1016/j.ejc.2011.04.004
fatcat:o6tyiyvfmbfdlfp7dzv5rwoeiq
*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*. ...##
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Countable connected-homogeneous graphs

2010
*
Journal of combinatorial theory. Series B (Print)
*

of

doi:10.1016/j.jctb.2009.04.002
fatcat:unuaac5ywzeazdmf32cd3yqwjy
*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*. ...##
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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. ...##
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Permutation monoids and MB-homogeneity for graphs and relational structures
[article]

2019
*
arXiv
*
pre-print

We also consider MB-

arXiv:1802.04166v2
fatcat:5tj67zxhvre7hlifnrsxgaevty
*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*. ...##
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Homogeneous coloured multipartite graphs

2014
*
European journal of combinatorics (Print)
*

We classify the

doi:10.1016/j.ejc.2014.06.006
fatcat:t2bbygfv6fbr5koupegs7g7xhq
*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*. ...##
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Connected-homomorphism-homogeneous graphs
[article]

2012
*
arXiv
*
pre-print

The finite C-II (connected-

arXiv:1207.4373v1
fatcat:lj5cidsn25eflm7jzumqllnyku
*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] . ...##
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Homogeneity and related topics: An extended bibliography
[article]

2021
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arXiv
*
pre-print

We give a bibliography of works relating to

arXiv:2111.15429v2
fatcat:di6lzukkvzdwlcvabb7lozrdha
*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. ...##
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Forthcoming papers

1991
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Discrete Mathematics
*

We show that (n, m)+ (n -1, m -4) for all m s [
the following problem is solved: Let G be a

doi:10.1016/0012-365x(91)90063-8
fatcat:yv6fsd3i3rgl3ccthj5vwdfhvy
*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. ...##
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Homogeneous and Ultrahomogeneous Linear Spaces

1998
*
Journal of combinatorial theory. Series A
*

We give a complete classification of all

doi:10.1006/jcta.1998.2887
fatcat:tsenlwojunhwfm3oztmxpig35i
*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*...##
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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 ...##
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Countable homogeneous linearly ordered posets

2012
*
European journal of combinatorics (Print)
*

We characterise all

doi:10.1016/j.ejc.2012.06.006
fatcat:edgwsymivvc3torxowim4gaaim
*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] . ...##
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Finite 3-connected homogeneous graphs
[article]

2018
*
arXiv
*
pre-print

In 1985, Cameron and Macpherson determined all finite (G, 3)-

arXiv:1810.01535v2
fatcat:xpe65toagrezboo4ueuowxo5mq
*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*. ...##
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Amenability and unique ergodicity of automorphism groups of countable homogeneous directed graphs
[article]

2017
*
arXiv
*
pre-print

We study the automorphism groups of

arXiv:1712.09461v1
fatcat:cu3eq6kxuncatip7qdcfgynrii
*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. ...##
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Complexities of relational structures
[article]

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. ...

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Homomorphism-homogeneous L-colored graphs
[article]

2012
*
arXiv
*
pre-print

A full classification of finite MH-

arXiv:1204.5879v1
fatcat:ds2ucyhmg5dzhord47zju4yupa
*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*...
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