Ramsey and anti-Ramsey structures in deterministic and random graphs
Structural and extremal properties of graphs and hypergraphs
Algorithmic and structural aspects of covering and packing problems on graphs
| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil
[2] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 - USA
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | RANDOM STRUCTURES & ALGORITHMS; v. 54, n. 2, p. 304-339, MAR 2019. |
| Web of Science Citations: | 2 |
| Abstract | |
For graphs G and F, write G -> (F)(l) if any coloring of the edges of G with l colors yields a monochromatic copy of the graph F. Suppose S-(h) is obtained from a graph S with s vertices and maximum degree d by subdividing its edges h times (that is, by replacing the edges of S by paths of length h + 1). We prove that there exists a graph G with no more than (log s)(20h)s(1+1/(h+1)) edges for which G -> (S-(h))(l) holds, provided that s >= s(0)(h, d, l). Wealso extend this result to the case in which Q is a graph with maximum degree d on q vertices with the property that every pair of vertices of degree greater than 2 are distance at least h + 1 apart. This complements work of Pak regarding the size Ramsey number of ``long subdivisions{''} of bounded degree graphs. (AU) | |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |