Increasing sequences with nonzero block sums and increasing paths in edge-ordered graphs
نویسندگان
چکیده
منابع مشابه
And Increasing Paths in Ktm~e-ordered Graphs
Consider the maximum length [(k) of a flexicographieally) increasing sequence of vectors in GF(2) k with the property that the sum of the vectors in any consecutive subsequence is nonzero modulo 2. We prove that ~ . 2 k ~<f(k)~<(~+o(1))2 k. A related problem is the following. Suppose the edges of the complete graph K , are labelled by the numbers 1,2 . . . . . (~.). What is the minimum a(n), ov...
متن کاملIncreasing Paths in Edge-Ordered Graphs: The Hypercube and Random Graph
An edge-ordering of a graph G = (V,E) is a bijection φ : E → {1, 2, . . . , |E|}. Given an edge-ordering, a sequence of edges P = e1, e2, . . . , ek is an increasing path if it is a path in G which satisfies φ(ei) < φ(ej) for all i < j. For a graph G, let f(G) be the largest integer ` such that every edge-ordering of G contains an increasing path of length `. The parameter f(G) was first studie...
متن کاملHamiltonian increasing paths in random edge orderings
Let f be an edge ordering of Kn: a bijection E(Kn) → {1, 2, . . . , ( n 2 ) }. For an edge e ∈ E(Kn), we call f(e) the label of e. An increasing path in Kn is a simple path (visiting each vertex at most once) such that the label on each edge is greater than the label on the previous edge. We let S(f) be the number of edges in the longest increasing path. Chvátal and Komlós raised the question o...
متن کاملMonotone paths in edge-ordered sparse graphs
An edge-ordered graph is an ordered pair (G, f), where G = G(V,E) is a graph and f is a bijective function, f : E(G) → {1, 2, ..., |E(G)|}. f is called an edge ordering of G. A monotone path of length k in (G, f) is a simple path Pk+1 : v1, v2..., vk+1 in G such that either, f((vi, vi+1)) < f((vi+1, vi+2)) or f((vi, vi+1)) > f((vi+1, vi+2)) for i = 1, 2, ..., k − 1. Given an undirected graph G,...
متن کاملMonotone Paths in Dense Edge-Ordered Graphs
The altitude of a graphG, denoted f(G), is the largest integer k such that under each ordering of E(G), there exists a path of length k which traverses edges in increasing order. In 1971, Chvátal and Komlós asked for f(Kn), where Kn is the complete graph on n vertices. In 1973, Graham and Kleitman proved that f(Kn) ≥ √ n− 3/4− 1/2 and in 1984, Calderbank, Chung, and Sturtevant proved that f(Kn)...
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: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90031-1