TAILIEUCHUNG - Báo cáo toán học: "Topological circles and Euler tours in locally finite graphs"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Topological circles and Euler tours in locally finite graphs. | Topological circles and Euler tours in locally finite graphs Agelos Georgakopoulos Mathematisches Seminar Universitat Hamburg Bundesstrafie 55 20146 Hamburg Germany Submitted Jan 15 2008 Accepted Mar 16 2009 Published Mar 25 2009 Mathematics Subject Classification 05C45 Abstract We obtain three results concerning topological paths ands circles in the end compactification G of a locally finite connected graph G. Confirming a conjecture of Diestel we show that through every edge set E EC there is a topological Euler tour a continuous map from the circle S1 to the end compactification G of G that traverses every edge in E exactly once and traverses no other edge. Second we show that for every sequence tì ì n of topological x-y paths in G there is a topological x-y path in G all of whose edges lie eventually in every member of some fixed subsequence of Tj . It is pointed out that this simple fact has several applications some of which reach out of the realm of G . Third we show that every set of edges not containing a finite odd cut of G extends to an element of C . 1 Introduction Erdos et al. 17 characterised the infinite graphs G containing an Euler tour that is a two-way infinite walk traversing every edge of G precisely once. Although their result is best possible it is not really satisfying graphs with more than two ends cannot have such an Euler tour so we cannot generalise to arbitrary infinite graphs the well-known theorems about Euler tours in finite ones. However Diestel and Kuhn 13 proposed a new concept of an Euler tour called a topological Euler tour that does allow such theorems to generalise to arbitrary infinite graphs at least locally finite ones. A topological Euler tour of a locally finite multi- graph G is a continuous map ơ S1 - G traversing every edge of G precisely once. Here G is the Freudenthal Supported by a GIF grant. THE ELECTRONIC JOURNAL OF COMBINATORICS 16 2009 R40 1 compactification 18 of G a topological space consisting of G and its .

TÀI LIỆU LIÊN QUAN
TỪ KHÓA LIÊN QUAN
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.