منابع مشابه
Endpoint extendable paths in dense graphs
Let G be a graph of order n. A path P of G is extendible if it can be extended to a longer path from one of its two endvertices, otherwise we say P is non-extendible. Let G be a graph of order n. We show that there exists a threshold number s such that every path of order smaller than s is extendible and there exists a non-extendible path of order t for each t ∈ {s, s+ 1, · · · , n} provided G ...
متن کاملEndpoint extendable paths in tournaments
Let s(n) be the threshold for which each directed path of order smaller than s ( n ) is extendible from one of its endpoints in some tournament T,. It is shown that s(n) is asymptotic to 3n/4, with an error term at most 3 for infinitely many n. There are six tournaments with s (n) = n.
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 کاملEdge cycle extendable graphs
A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C is also formed from edges and one chord of a cycle C ′ of length one greater than C with V (C ) ⊆ V (C). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivale...
متن کاملImproved Bounds for Shortest Paths in Dense Distance Graphs
We study the problem of computing shortest paths in so-called dense distance graphs. Every planar graph G on n vertices can be partitioned into a set of O(n/r) edge-disjoint regions (called an r-division) with O(r) vertices each, such that each region has O( √ r) vertices (called boundary vertices) in common with other regions. A dense distance graph of a region is a complete graph containing a...
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: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.09.014