Infinite paths in planar graphs IV, dividing cycles
نویسندگان
چکیده
منابع مشابه
Infinite paths in planar graphs IV, dividing cycles
Nash-Williams conjectured that a 4-connected infinite planar graph contains a spanning 2-way infinite path if, and only if, the deletion of any finite set of vertices results in at most two infinite components. In this paper, we prove the Nash-Williams conjecture for graphs with no dividing cycles and for graphs with infinitely many vertex disjoint dividing cycles. A cycle in an infinite plane ...
متن کاملInfinite paths in planar graphs III, 1-way infinite paths
An infinite graph is 2-indivisible if the deletion of any finite set of vertices from the graph results in exactly one infinite component. Let G be a 4-connected, 2indivisible, infinite, plane graph. It is known that G contains a spanning 1-way infinite path. In this paper, we prove a stronger result by showing that, for any vertex x and any edge e on a facial cycle of G, there is a spanning 1-...
متن کاملSpanning paths in infinite planar graphs
Let G be a 4-connected infinite planar graph such that the deletion of any finite set of vertices of G results in at most one infinite component. We prove a conjecture of Nash-Williams that G has a 1-way infinite spanning path. c © 1996 John Wiley
متن کاملHamiltonian Paths and Cycles in Planar Graphs
We examine the problem of counting the number of Hamiltonian paths and Hamiltonian cycles in outerplanar graphs and planar graphs, respectively. We give an O(nαn) upper bound and an Ω(αn) lower bound on the maximum number of Hamiltonian paths in an outerplanar graph with n vertices, where α ≈ 1.46557 is the unique real root of α = α + 1. For any positive integer n ≥ 6, we define an outerplanar ...
متن کاملInfinite paths in planar graphs I: Graphs with radial nets
Let G be an infinite 4-connected planar graph such that the deletion of any finite set of vertices from G results in exactly one infinite component. Dean et al proved that either G admits a radial net or a special subgraph of G admits a ladder net, and they used these nets to show that G contains a spanning 1-way infinite path. In this paper, we show that if G admits a radial net, then G also c...
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: Journal of Graph Theory
سال: 2006
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.20176