Extending Cycles Locally to Hamilton Cycles
نویسندگان
چکیده
منابع مشابه
Extending Cycles Locally to Hamilton Cycles
A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle S1 that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs. Furthermore, we show that such graphs are Hamilton-connected if and only if they are 3-...
متن کاملHamilton Cycles in Planar Locally Finite Graphs
A classical theorem by Tutte assures the existence of a Hamilton cycle in every finite 4-connected planar graph. Extensions of this result to infinite graphs require a suitable concept of an infinite cycle. Such a concept was provided by Diestel and Kühn, who defined circles to be homeomorphic images of the unit circle in the Freudenthal compactification of the (locally finite) graph. With this...
متن کاملInfinite Hamilton Cycles in Squares of Locally Finite Graphs
We prove Diestel’s conjecture that the square G of a 2-connected locally finite graph G has a Hamilton circle, a homeomorphic copy of the complex unit circle S in the Freudenthal compactification of G.
متن کاملPacking Hamilton Cycles Online
It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge disjoint Hamilton cycles, [4], [13], [9]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to color the edges online with σ color...
متن کاملEdge Disjoint Hamilton Cycles
In the late 70s, it was shown by Komlós and Szemerédi ([7]) that for p = lnn+ln lnn+c n , the limit probability for G(n, p) to contain a Hamilton cycle equals the limit probability for G(n, p) to have minimum degree at least 2. A few years later, Ajtai, Komlós and Szemerédi ([1]) have shown a hitting time version of this in the G(n,m) model. Say a graph G has property H if it contains bδ(G)/2c ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/3960