𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On large induced trees and long induced paths in sparse random graphs

✍ Scribed by W.C.Stephen Suen


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
697 KB
Volume
56
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Maximal induced trees in sparse random g
✍ Tomasz Ε‚uczak; Zbigniew Palka πŸ“‚ Article πŸ“… 1988 πŸ› Elsevier Science 🌐 English βš– 493 KB

A study of the orders of maximal induced trees in a random graph G, with small edge probability p is given. In particular, it is shown that the giant component of almost every G,, where p = c/n and c > 1 is a constant, contains only very small maximal trees (that are of a specific type) and very lar

The largest induced tree in a sparse ran
✍ W. Fernandez de la Vega πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 192 KB πŸ‘ 2 views

The author proved that, for c > 1, the random graph G(n, p ) on n vertices with edge probability p = c / n contains almost always an induced tree on at least q n ( 1 -o( 1)) vertices, where L Y ~ is the positive root of the equation CLY = log( 1 + c'a). It is shown here that if c is sufficiently lar

Large induced forests in sparse graphs
✍ Noga Alon; Dhruv Mubayi; Robin Thomas πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 148 KB

## Abstract For a graph __G__, let __a__(__G__) denote the maximum size of a subset of vertices that induces a forest. Suppose that __G__ is connected with __n__ vertices, __e__ edges, and maximum degree Ξ”. Our results include: (a) if Δ ≀ 3, and __G__ ≠ __K__~4~, then __a__(__G__) β‰₯ __n__β€‰βˆ’β€‰e/4β€‰βˆ’β€‰1

Subdivisions of large complete bipartite
✍ Thomas BΓΆhme; Bojan Mohar; Riste Ε krekovski; Michael Stiebitz πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 67 KB πŸ‘ 1 views

## Abstract It is proved that for every positive integers __k__, __r__ and __s__ there exists an integer __n__ = __n__(__k__,__r__,__s__) such that every __k__‐connected graph of order at least __n__ contains either an induced path of length __s__ or a subdivision of the complete bipartite graph __

Some results on graphs without long indu
✍ Dong, Jinquan πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 294 KB πŸ‘ 2 views

Let I(t) be the set of integers with the property that in every Pt-free connected graph G, the i-center C,(G) induces a connected subgraph. What is the minimum element of /(t)? In this paper, we prove that this minimum is [2t/3] -1 if t = 0 or Z(mod3) and is [ 2 t / 3 ] otherwise. Furthermore, as co