# On the Ramsey Numbers of Odd-Linked Double Stars

@inproceedings{Karamchedu2021OnTR, title={On the Ramsey Numbers of Odd-Linked Double Stars}, author={Chaitanya D. Karamchedu and Maria M. Klawe}, year={2021} }

The linked double star Sc(n,m), where n ≥ m ≥ 0, is the graph consisting of the union of two stars K1,n and K1,m with a path on c vertices joining the centers. Its ramsey number r(Sc(n,m)) is the smallest integer r such that every 2-coloring of the edges of a Kr admits a monochromaticSc(n,m). In this paper, we study the ramsey numbers of linked double stars when c is odd. In particular, we establish bounds on the value of r(Sc(n,m)) and determine the exact value of r(Sc(n,m)) if n ≥ c, or if n…

## References

SHOWING 1-10 OF 10 REFERENCES

Generalized ramsey theory for graphs, x: double stars

- Computer Science, MathematicsDiscret. Math.
- 1979

It is shown that r(S(n, m)) = max (2n + 1, n + 2m + 2) if n is odd and mÂ?2 and r(N, m), which is the least number p such that there is a monochromatic copy of S( n, m) in any 2-coloring of the edges of Kp.

Asymptotics of Ramsey numbers of double stars

- Mathematics
- 2016

A double star $S(n,m)$ is the graph obtained by joining the center of a star with $n$ leaves to a center of a star with $m$ leaves by an edge. Let $r(S(n,m))$ denote the Ramsey number of the double…

On a ramsey-type problem of J. A. Bondy and P. Erdös. I

- Mathematics
- 1973

Let R(Cn, Cp) be the smallest integer m for which the following statement is true: If a G graph has at least m vertices, then either G contains a Cn (cycle of length n) or G contains a Cp.
Bondy…

Generalized Ramsey theory for graphs

- Mathematics
- 1972

The classical Ramsey numbers [7] involve the occurrence of monochromatic complete subgraphs in line-colored complete graphs. By removing the completeness requirements and admitting arbitrary…

Path-Star Ramsey numbers

- Mathematics
- 1974

Abstract Let f ( m , n ) be the least integer N such that for every graph G with N vertices, either G contains a path of m vertices or the complement of G contains a vertex of degree at least n .…

All Ramsey numbers for cycles in graphs

- Mathematics, Computer ScienceDiscret. Math.
- 1974

The Ramsey number problem for cycles is complete by verifying the previously conjectured values of r and s by verifying their previously conjecturing values.

Extremal Ramsey theory for graphs

- 1976

If G and H are graphs, define the Ramsey number to be the least number p such that if the lines of the complete graph Kp are colored red and blue (say),either the red subgraph contains a copy of G or…

All Ramsey Numbers for Brooms in Graphs

- Computer Science, MathematicsElectron. J. Comb.
- 2016

The value of R(B_{n-\ell,\ell}) is determined in this paper to attain the maximum and minimum values of $R(T_n)$ as $\ell$ varies.

Cycles in bipartite graphs

- Computer Science, MathematicsJ. Comb. Theory, Ser. B
- 1981

This paper proves two results concerning the existence of cycles in G(a, b, k) - a simple bipartite graph with bipartition (A, B).

Small Ramsey Numbers

- Mathematics
- 2011

We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are…