✦ LIBER ✦

On the number of induced subgraphs of a random graph

✍ Scribed by Hiroshi Maehara

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 175 KB
Volume: 64
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90201-9

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On the number of distinct induced subgra

On the number of distinct induced subgraphs of a graph

✍ P. Erdős; A. Hajnal 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 582 KB

On the number of maximal bipartite subgr

On the number of maximal bipartite subgraphs of a graph

✍ Jesper Makholm Byskov; Bolette Ammitzbøll Madsen; Bjarke Skjernaa 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 72 KB 👁 2 views

We show new lower and upper bounds on the maximum number of maximal induced bipartite subgraphs of graphs with n vertices. We present an infinite family of graphs having 105 n=10 % 1:5926 n ; such subgraphs show an upper bound of O(12 n=4 ) ¼ O(1:8613 n ) and give an algorithm that finds all maximal

Graphs with a small number of distinct i

Graphs with a small number of distinct induced subgraphs

✍ Noga Alon; Béla Bollobás 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 514 KB

Let G be a graph on n vertices. We show that if the total number of isomorphism types of induced subgraphs of G is at most &II', where E < lo-\*', then either G or its complement contain an independent set on at least (1 -4e)n vertices. This settles a problem of Erdiis and Hajnal.

On the Density of Subgraphs in a Graph w

On the Density of Subgraphs in a Graph with Bounded Independence Number

✍ Pavel Valtr 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 260 KB

Let \_(n, m, k) be the largest number \_ # [0, 1] such that any graph on n vertices with independence number at most m has a subgraph on k vertices with at lest \_ } ( k 2 ) edges. Up to a constant multiplicative factor, we determine \_(n, m, k) for all n, m, k. For log n m=k n, our result gives \_(

On the chromatic number of a random 5-re

On the chromatic number of a random 5-regular graph

✍ J. Díaz; A. C. Kaporis; G. D. Kemkes; L. M. Kirousis; X. Pérez; N. Wormald 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 275 KB 👁 1 views

## Abstract It was only recently shown by Shi and Wormald, using the differential equation method to analyze an appropriate algorithm, that a random 5‐regular graph asymptotically almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5‐regular graph is as

On the number of hamilton cycles in a ra

On the number of hamilton cycles in a random graph

✍ C. Cooper; A. M. Frieze 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 576 KB

Let a random graph G be constructed by adding random edges one by one, starting with n isolated vertices. We show that with probability going to one as n goes to infinity, when G first has minimum degree two, it has at least (log n)('-')" distinct hamilton cycles for any fixed E > 0.