An infinite family of T-factorizations of complete graphs , where 2n = 56k and k is a positive integer, in which the set of vertices of T can be split into two subsets of the same cardinality such that degree sums of vertices in both subsets are not equal, is presented. The existence of such T-factorizations provides a negative answer to the problem posed by Kubesa.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1413,
author = {Mariusz Meszka},
title = {Solution to the problem of Kubesa},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {375-378},
zbl = {1209.05188},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1413}
}
Mariusz Meszka. Solution to the problem of Kubesa. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 375-378. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1413/
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