Partitioning edge-2-colored graphs into monochromatic paths and cycles

Document Type

Presentation Abstract

Presentation Date

9-15-2014

Abstract

We are given a graph G and its edges are colored with two colors. How many vertex-disjoint monochromatic paths/cycles are needed to cover its vertices? We prove several theorems. We show that two times the independence number many cycles are always enough to cover almost all vertices of G. Furthermore, if the minimum degree is at least 3n/4, then 2 cycles can cover almost all vertices of G. Finally, if the graph does not contain a forbidden bipartite subgraph, then 2 paths can cover almost all the vertices of G. (joint work with J. Balogh, J. Barát, A. Gyárfás, G. Sárközy)

Additional Details

Monday, September 15, 2014 at 3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

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