Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Mathematics
Note On Highly Connected Monochromatic Subgraphs In 2-Colored Complete Graphs, Shinya Fujita, Colton Magnant
Note On Highly Connected Monochromatic Subgraphs In 2-Colored Complete Graphs, Shinya Fujita, Colton Magnant
Colton Magnant
In this note, we improve upon some recent results concerning the existence of large monochromatic, highly connected subgraphs in a 2-coloring of a complete graph. In particular, we show that if n≥6.5(k−1), then in any 2-coloring of the edges of Kn, there exists a monochromatic k-connected subgraph of order at least n−2(k−1). Our result improves upon several recent results by a variety of authors.
Coloring Rectangular Blocks In 3-Space, Colton Magnant, Daniel M. Martin
Coloring Rectangular Blocks In 3-Space, Colton Magnant, Daniel M. Martin
Colton Magnant
If rooms in an office building are allowed to be any rectangular solid, how many colors does it take to paint any configuration of rooms so that no two rooms sharing a wall or ceiling/floor get the same color? In this work, we provide a new construction which shows this number can be arbitrarily large.