Robert A. Krueger

activity

20182020

collaborators

6 papers

math.CO2020

A note about monochromatic components in graphs of large minimum degree

Louis DeBiasio, Robert A. Krueger

For all positive integers $r \geq 3$ and $n$ such that $r^{2} - r$ divides $n$ and an affine plane of order $r$ exists, we construct an $r$ -edge colored graph with minimum degree $(1-\f…

math.CO2019

Generalized Ramsey numbers: forbidding paths with few colors

Robert A. Krueger

Let $f (K_{n}, H, q)$ be the minimum number of colors needed to edge-color $K_{n}$ so that every copy of $H$ is colored with at least $q$ colors. Originally posed by Erdős and Shelah wh…

math.CO2018

Partitioning the power set of $[n]$ into $C_{k}$ -free parts

Eben Blaisdell, András Gyárfás, Robert A. Krueger +1

We show that for $n \geq 3, n \neq = 5$ , in any partition of $P (n)$ , the set of all subsets of $[n] = {1, 2, \dots, n}$ , into $2^{n - 2} - 1$ parts, some part must contain a triangl…

math.CO2018

Long monochromatic paths and cycles in 2-colored bipartite graphs

Louis DeBiasio, Robert A. Krueger

Gyárfás and Lehel and independently Faudree and Schelp proved that in any 2-coloring of the edges of $K_{n, n}$ there exists a monochromatic path on at least $2 ⌈ n /2 ⌉$ ver…

math.CO2018

Large monochromatic components in multicolored bipartite graphs

Louis DeBiasio, Robert A. Krueger, Gábor N. Sárközy

It is well-known that in every $r$ -coloring of the edges of the complete bipartite graph $K_{m, n}$ there is a monochromatic connected component with at least $\frac{m + n}{r}$ vertice…

math.CO2018

Monochromatic balanced components, matchings, and paths in multicolored complete bipartite graphs

Louis DeBiasio, András Gyárfás, Robert A. Krueger +2

It is well-known that in every $r$ -coloring of the edges of the complete bipartite graph $K_{n, n}$ there is a monochromatic connected component with at least $\frac{2 n}{r}$ vertices…

A note about monochromatic components in graphs of large minimum degree

Generalized Ramsey numbers: forbidding paths with few colors

Partitioning the power set of [n] into Ck​-free parts

Long monochromatic paths and cycles in 2-colored bipartite graphs

Large monochromatic components in multicolored bipartite graphs

Monochromatic balanced components, matchings, and paths in multicolored complete bipartite graphs

Partitioning the power set of $[n]$ into $C_{k}$ -free parts