Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Fox, B. Sudakov (2007)
Density theorems for bipartite graphs and related Ramsey-type resultsCombinatorica, 29
Chaoping Pei, Yusheng Li (2016)
Ramsey numbers involving a long pathDiscret. Math., 339
V. Nikiforov, C. Rousseau (2007)
Ramsey goodness and beyondCombinatorica, 29
Lianmin Zhang, Yaojun Chen, T. Cheng (2010)
The Ramsey numbers for cycles versus wheels of even orderEur. J. Comb., 31
Peter Allen, G. Brightwell, J. Skokan (2010)
Ramsey-goodness—and otherwiseCombinatorica, 33
(1973)
Ramsey number for cycles in graphs
(2012)
Sudakov,B.:On twoproblems in graphRamsey
C. Chvatál, V. Rödl, E. Szemerédi, W. Trotter (1983)
The Ramsey number of a graph with bounded maximum degreeJ. Comb. Theory, Ser. B, 34
A. Pokrovskiy (2013)
Calculating Ramsey Numbers by Partitioning Colored GraphsJournal of Graph Theory, 84
D Conlon, J Fox, B Sudakov (2012)
On two problems in graph Ramsey theoryCombinatorica, 32
R. Graham, V. Rödl, A. Rucinski (2000)
On graphs with linear Ramsey numbersJ. Graph Theory, 35
S. Burr (1981)
Ramsey Numbers Involving Graphs with Long Suspended PathsJournal of The London Mathematical Society-second Series
A connected graph H with $$|H|\ge \sigma (G)$$ | H | ≥ σ ( G ) is said to be G-good if $$R(G,H)=(\chi (G)-1)(|H|-1)+\sigma (G)$$ R ( G , H ) = ( χ ( G ) - 1 ) ( | H | - 1 ) + σ ( G ) . For an integer $$\ell \ge 3$$ ℓ ≥ 3 , let $$P_\ell $$ P ℓ be a path of order $$\ell $$ ℓ , and $$H^{(\ell )}$$ H ( ℓ ) a graph obtained from H by joining the end vertices of $$P_\ell $$ P ℓ to distinct vertices u, v of H. It is widely known that for any graphs G and H, if $$\ell $$ ℓ is sufficiently large, then $$H^{(\ell )}$$ H ( ℓ ) is G-good. In this note, we show that there exists a constant $$c=c(\Delta )$$ c = c ( Δ ) such that for any graphs G and H with $$\Delta (G)\le \Delta $$ Δ ( G ) ≤ Δ and $$\Delta (H)\le \Delta $$ Δ ( H ) ≤ Δ , if $$\ell \ge c\cdot (|G|+|H|)$$ ℓ ≥ c · ( | G | + | H | ) , then $$H^{(\ell )}$$ H ( ℓ ) is G-good; and if $$n\ge 2\alpha (G)+\Delta ^2(G)+4$$ n ≥ 2 α ( G ) + Δ 2 ( G ) + 4 , then $$P_n$$ P n is G-good.
Graphs and Combinatorics – Springer Journals
Published: Jun 6, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.