Long correlated paths
نویسندگان
چکیده
منابع مشابه
Connected graphs without long paths
A problem, first considered by Erdős and Gallai [2], was to determine the maximum number of edges in any graph on n vertices if it contains no path with k + 1 vertices. This maximum number, ext(n, Pk+1), is called the extremal number for the path Pk+1. Erdős and Gallai proved the following theorem, which was one of the earliest extremal results in graph theory. Theorem 1.1 ([2]). For every k ≥ ...
متن کاملDecomposing Graphs into Long Paths
It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C3, C4, C5, and K4 − e have no such decompositions. We construct an infinite sequence {Fi}∞i=0 of nondecomposable graphs. On the other hand, we prove that every...
متن کاملUniversal properties of shortest paths in isotropically correlated random potentials
We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numer...
متن کاملLong Alternating Paths in Bicolored Point Sets
Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length n + c √ n logn . We disprove a conjecture of Erdős by constructing an example without any such path of length greater than 4 3 n+ c′ √ n.
متن کاملLong cycles and paths in distance graphs
For n ∈ N and D ⊆ N, the distance graph P n has vertex set {0, 1, . . . , n− 1} and edge set {ij | 0 ≤ i, j ≤ n − 1, |j − i| ∈ D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs. A fundamental result concerning circulant graphs is that for these graphs, a simple greatest common divisor condition, their connectivity, and the existence of ...
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: Nature Nanotechnology
سال: 2016
ISSN: 1748-3387,1748-3395
DOI: 10.1038/nnano.2016.218