If G is a finite abelian group and n ) 1 is an integer, we say that G has the Hajos n-property, or is n-good if from each decomposition G s S S . . . S of G ´1 2 n into a direct product of subsets, it follows that at least one of the S is periodic, i Ä 4 meaning that there exists x g G y e such that
Hajós factorizations and completion of codes
✍ Scribed by Nguyen Huong Lam
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 804 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
✦ Synopsis
Given a Haj6s factorization of Z,, De Felice has shown that an + Jb + bag is finitely completable to a d-code, d <3. In this article, we prove that the code u" + aPbaQ is finitely completable but not always to a d-code with d < 3.
📜 SIMILAR VOLUMES
## Abstract In his recent work Thomassen [J Combin Theory Ser B 93 (2005), 95–105] discussed various refinements of Hajós conjecture. Shortly after Mohar [Electr J Combin 12 (2005), N15] provided an answer to Thomassen's Conjecture 6.5, and proposed a possible extension. The aim of this article is
Let A \* be a free monoid generated by a set A and let X ⊆ A \* be a code with property P. The embedding of X into a complete code Y ⊆ A \* with the same property P is called the completion of X . The method of completion of rational biÿx codes and codes with ÿnite decoding delays have been investig
## Seyffarth, K., Hajos' conjecture and small cycle double covers of planar graphs, Discrete Mathematics 101 (1992) 291-306. We prove that every simple even planar graph on n vertices has a partition of its edge set into at most [(n -1)/2] cycles. A previous proof of this result was given by Tao,
We show that an infinite word s satisfies s = uoutu2 . . . with all ui being different nonempty words and their set being a biprefix code if and only if s is not ultimately periodic. We give also related results, considering in particular arbitrary codes, infix codes and the case of two-sided infini