HOW PROVABLY GRACEFUL ARE THE TREES?
Abstrak: The
Ringel-Kotzig-Rosa conjecture that all trees are graceful, originating in Ringel
[3] and Rosa [4] is nearing 50 years without being resolved. Much evidencehas
been produced in support of the conjecture (see Gallian [2]), the majority of which
falls under the \Here is another family of graceful trees" or \Trees of
this type are graceful, and as the order of these trees increases the number of
ways to gracefully label them increases" categories. But what can be said
about all trees? Do they all possess a property that is close to being
graceful? Is there a numerical measure by which we can say \All trees are at
least this graceful" ? Two open problems of this nature follow.
Author: Peter J. Slater
Journal Code: jpmatematikagg110006
