zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Sailing towards, and then against, the graceful tree conjecture: some promisuous results. (English) Zbl 1163.05007
Summary: The graceful tree conjecture is getting old – though 40 years are not so many – while researchers from all over the world keep on trying to put an affirmative end to it. Kotzig called a disease the effort of proving it. In this paper we fall into the opposite disease, by shyly moving towards the search of a tree that is not graceful. Our first result, on suitable attachments of graceful trees, does actually produce new graceful trees. But the reader might perceive a subtle friction between the combinatorial structure and the arithmetical need of achieving a graceful labelling (that sensation sound perhaps like a warning). Subsequently, the classification of all graceful labellings for a rather simple class of trees seem at a first glance reassuring for its richness, while a more careful analysis may highlight some heavy constraints for labels, due to the mere structure of trees. Here the question is: what could happen to label constraints if the tree has a wilder structure? Should we give up gracefulness? In the end we turn our cards over and introduce a polynomial associated to a given tree, which is expected to help the willing researcher to find some ungraceful tree, if any, in the next future.
MSC:
05C05Trees
05C78Graph labelling