Mutually embeddable graphs and the tree alternative conjecture
نویسندگان
چکیده
We prove that if a rayless tree T is mutually embeddable and non-isomorphic with another rayless tree, then T is mutually embeddable and non-isomorphic with infinitely many rayless trees. The proof relies on a fixed element theorem of Halin, which states that every rayless tree has either a vertex or an edge that is fixed by every self-embedding. We state a conjecture that proposes an extension of our result to all trees.
منابع مشابه
A proof of the rooted tree alternative conjecture
In [2] Bonato and Tardif conjectured that the number of isomorphism classes of trees mutually embeddable with a given tree T is either 1 or ∞. We prove the analogue of their conjecture for rooted trees. We also discuss the original conjecture for locally finite trees and state some new conjectures.
متن کاملClosed 2-cell embeddings of 4 cross-cap embeddable graphs
The strong embedding conjecture states that every 2-connected graph has a closed 2-cell embedding in some surface , i . e . an embedding that each face is bounded by a circuit in the graph . A graph is called k -crosscap embeddable if it can be embedded in the surface of non-orientable genus k . We confirm the strong embedding conjecture for 5-crosscap embeddable graphs . As a corollary , every...
متن کامل-λ coloring of graphs and Conjecture Δ ^ 2
For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...
متن کاملA Characterization of Upper-embeddable Graphs
It is proved that a pseudograph G is upper-embeddable if and only if it has a spanning tree T such that G — T has at most one component with an odd number of edges. This result is then used to show that all 4-edge connected graphs are upper-embeddable.
متن کاملD - Width , Metric Embedding , and Their Connections
Embedding between metric spaces is a very powerful algorithmic tool and has been used for finding good approximation algorithms for several problems. In particular, embedding to an l1 norm has been used as the key step in an approximation algorithm for the sparsest cut problem. The sparsest cut problem, in turn, is the main ingredient of many algorithms that have a divide and conquer nature and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 96 شماره
صفحات -
تاریخ انتشار 2006