论文信息 - Self-embeddings of trees

Self-embeddings of trees

We prove a fix point theorem for monoids of self-embeddings of trees. As a corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either contains a subdivided binary tree as a subtree or has a vertex, and edge, an end or two ends fixed by all its self-embeddings.

Matthias Hamann

[1] Rgnvaldur G. Mller. Ends of graphs , 1992, Mathematical Proceedings of the Cambridge Philosophical Society.

[2] M. Pavone. Bilateral denseness of the hyperbolic limit points of groups acting on metric spaces , 1997 .

[3] Reinhard Diestel,et al. Locally finite graphs with ends: A topological approach, III. Fundamental group and homology , 2010, Discret. Math..

[4] R. Halin,et al. Automorphisms and endomorphisms of infinite locally finite graphs , 1973 .

[5] Maya Stein,et al. Ends of graphs , 2005 .

[6] Wolfgang Woess,et al. Fixed sets and free subgroups of groups acting on metric spaces , 1993 .

[7] Reinhard Diestel,et al. Locally finite graphs with ends: A topological approach, II. Applications , 2010, Discret. Math..

[8] H. A. Jung,et al. On finite fixed sets in infinite graphs , 1994, Discret. Math..

[9] Wolfgang Woess. Amenable group actions on infinite graphs , 1989 .

[10] Maurice Pouzet,et al. Invariant subsets of scattered trees. An application to the tree alternative property of Bonato and Tardif , 2015, 1508.01123.

[11] Anthony Bonato,et al. Mutually embeddable graphs and the tree alternative conjecture , 2006, J. Comb. Theory, Ser. B.

[12] Reinhard Diestel,et al. Locally finite graphs with ends: A topological approach, I. Basic theory , 2009, Discret. Math..