… The thickness of a graph G, is the minimum number of planar graphs, whose union is G.
Halton conjectured that any graph of maximum degree d has thickness at most ⌈(d+2)/4⌉ …

… Notes and acknowledgements. The 'three lengths theorem', equivalent to the first … as a
conjecture of H. Steinhaus, and was proved by Swierczkowski in (5). He also proved a conjecture …

… of a finite-difference approximation to the problem shows that a … a family of solutions with
M — 1 continuous parameters exists for the finite-difference problem. With the above conjecture …

… We offer a new proof of the Steinhaus Conjecture which states that, for all irrational a and all
N, … The proof offered by Halton [2] involves a description of the dynamics of the gap division …

… from Halton's article that imply the claimed upper bound. Lemma 3 2 describes the possibility
to augment a given graph to a regular … We close this note by giving the following conjecture. …

… extended version of (3) is that all the absolute kj(k— l)th moments of the probability distribution
should exist; and we conjecture that this is also a sufficient condition. Unfortunately, we …

… David A. Plairted for several stimulating dixussions in the first half-year of this period, as a
result of which he dericled Corollary 4 and conjectured Corollary 5. More recently, he has …

… counterexamples to two conjectures known in … Halton conjectured that any graph of maximum
degree 6 has thickness at most 2, ie it is biplanar. A supporting argument for the conjecture …

… We have run a test on a digital computer that shows k(p2) = k(… The question is closely
related to another one, “can a … proof, consult the papers by JH Halton [23] and JE Desmond […

… disprove a conjecture of JH Halton and suggest a conjecture on the improvement of a … To
estimate this last sum, we first note that if the string N (read from right to left) starts with a block …