𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A computational attack on the conjectures of Graffiti: New counterexamples and proofs

✍ Scribed by Tony L. Brewster; Michael J. Dinneen; Vance Faber

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
788 KB
Volume
147
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Graffiti is a computer program that checks for relationships among certain graph invariants. It uses a database of graphs and has generated well over 700 conjectures. Having obtained a readily available computer tape of all the nonisomorphic graphs with 10 or fewer vertices, we have tested approximately 200 of the Graffiti conjectures and have found counterexamples for over 40 of them. For each conjecture that failed we display a counterexample. We also provide results that came from analyzing those conjectures which had a small number of counterexamples. Finally, we prove some results about four of the conjectures.

πŸ“œ SIMILAR VOLUMES

A Proof of the Welch and Niho Conjecture
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences
✍ Henk D.L. Hollmann; Qing Xiang πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 412 KB

Binary m-sequences are widely applied in navigation, radar, and communication systems because of their nice autocorrelation and cross-correlation properties. In this paper, we consider the cross-correlation between a binary m-sequence of length 2K!1 and a decimation of that sequence by an integer t.

Proof of a Conjecture of BollobΓ‘s and Ko
Proof of a Conjecture of BollobΓ‘s and Kohayakawa on the ErdΕ‘s–Stone Theorem
✍ Yoshiyasu Ishigami πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 242 KB

For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .

Transglycosylation and multiple attack o
Transglycosylation and multiple attack of endo-(1β†’3)-Ξ²-d-glucanase L-IV from Spisula sachalinensis: A new approach to the evaluation of the degree of multiple attack on polysaccharides
✍ Peter W. Bezukladnikov; Lyudmila A. Elyakova πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 553 KB

The marked capability for transglycosylation by the endo-(1 +3)-D-D-glucanase L-IV from Spisula sachalinensis to glycerol, D-glucose, methyl a-and p-o-glucopyranoside, and methyl cellobioside as acceptors was employed to study the multiple attack of the enzyme on laminarin. The enzyme hydrolyses, on