Abstract

KRIEL, Christo  and  MPHAKO-BANDA, Eunice. Sizes of flats of cycle matroids of complete graphs. Rev.colomb.mat. [online]. 2022, vol.56, n.1, pp.63-75.  Epub Feb 04, 2023. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v56n1.105617.

We show that the problem of counting the number of flats of size k for a cycle matroid of a complete graph is equivalent to the problem of counting the number of partitions of an integer k into triangular numbers. In addition, we give some values of k such that there is no flat of size k in a cycle matroid of a complete graph of order n. Finally, we give a minimum bound for the number of values, k, for which there are no flats of size k in the given cycle matroid.

Keywords : Compositions; cycle matroid; flats; triangular number partitions; bad colouring.

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