A classification of connected-homogeneous digraphs

We classify the connected-homogeneous digraphs with more than one end. We further show that if their underlying undirected graph is not connected-homogeneous, they are highly-arc-transitive.

[1]  Rögnvaldur G. Möller.  Distance-Transitivity in Infinite Graphs , 1994, J. Comb. Theory, Ser. B.

[2]  Hikoe Enomoto,et al.  Combinatorially homogeneous graphs , 1981, J. Comb. Theory, Ser. B.

[3]  Norbert Seifter,et al.  Highly Arc-Transitive Digraphs With No Homomorphism Onto Z , 2002, Comb..

[4]  Norbert Seifter,et al.  Highly arc transitive digraphs: reachability, topological groups , 2005, Eur. J. Comb..

[5]  Rögnvaldur G. Möller.  Accessibility and Ends of Graphs , 1996, J. Comb. Theory, Ser. B.

[6]  Bernhard Krön,et al.  Cutting up graphs revisited – a short proof of Stallings' structure theorem , 2010, Groups Complex. Cryptol..

[7]  Julian Pott,et al.  Transitivity conditions in infinite graphs , 2009, Comb..

[8]  G. Cherlin,et al.  The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous N-Tournaments , 1998 .

[9]  Po-Shen Loh,et al.  Probabilistic Methods in Combinatorics , 2009 .

[10]  R. G. Möller,et al.  Groups '93 Galway / St Andrews: Groups acting on locally finite graphs - a survey of the infinitely ended case , 1995 .

[11]  Robert Gray,et al.  Countable connected-homogeneous graphs , 2010, J. Comb. Theory, Ser. B.

[12]  Warren Dicks,et al.  Groups Acting on Graphs , 1989 .

[13]  Martin Goldstern,et al.  Infinite homogeneous bipartite graphs with unequal sides , 1996, Discret. Math..

[14]  G. Cherlin.  Homogeneous tournaments revisited , 1988 .

[15]  M. J. Dunwoody.  Cutting up graphs , 1982, Comb..

[16]  P. M. Cohn,et al.  GROUPS ACTING ON GRAPHS (Cambridge Studies in Advanced Mathematics 17) , 1990 .

[17]  H. D. Macpherson.  Infinite distance transitive graphs of finite valency , 1982, Comb..

[18]  H. A. Jung,et al.  On vertex transitive graphs of infinite degree , 1993 .

[19]  Rögnvaldur G. Möller,et al.  Locally-finite connected-homogeneous digraphs , 2010, Discret. Math..

[20]  A. Gardiner.  Homogeneity conditions in graphs , 1978, J. Comb. Theory, Ser. B.

[21]  R. Woodrow,et al.  Countable ultrahomogeneous undirected graphs , 1980 .

[22]  M. Hamann.  End-transitive graphs , 2010, 1003.3665.

[23]  Norbert Seifter,et al.  Transitive digraphs with more than one end , 2008, Discret. Math..

[24]  Carsten Thomassen,et al.  Vertex-Transitive Graphs and Accessibility , 1993, J. Comb. Theory, Ser. B.

[25]  Cheryl E. Praeger,et al.  Infinite highly arc transitive digraphs and universal covering digraphs , 1993, Comb..

[26]  Christian Ronse,et al.  On Homogeneous Graphs , 1978 .

[27]  J. Spencer.  Probabilistic Methods in Combinatorics , 1974 .

[28]  A. H. Lachlan.  Finite Homogeneous Simple Digraphs , 1982 .

[29]  A. H. Lachlan,et al.  Countable homogeneous tournaments , 1984 .