A coloring problem for intersecting vector spaces

作者：Hoppen Carlos^*; Lefmann Hanno; Odermann Knut

来源：Discrete Mathematics, 2016, 339(12): 2941-2954.

DOI：10.1016/j.disc.2016.06.007

• Finite vector spaces
• Erdos-Ko-Rado Theorem
• Coloring
• Stability

In Hoppen et al. (2012) Kohayakawa and two of the current authors considered a variant of the classical Erclos-Ko-Rado problem for families of l-intersecting r-sets in which they asked for the maximum number of edge-colorings of an n-vertex r-uniform hypergraph such that all color classes are-intersecting. This resulted in a fairly complete characterization of the corresponding extremal families. In this paper, we show that, when the number of colors is k is an element of {2, 3, 4}, similar results may be obtained in the context of vector spaces. In particular, we observe that a rather unusual instability phenomenon occurs for k = 4 colors, namely that the problem is unstable despite admitting a unique extremal configuration up to isomorphism.

• 出版日期2016-12-6