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Ramsey-Type Results for Oriented Trees

, 2007
. For a graph G and a digraph ~ H, we write G! ~ H (respectively, G a ! ~ H) if every orientation (respectively, acyclic orientation) of the edges of G results in an induced copy of ~ H. In this note we study how small the graphs G such that G!
Vojtech Rödl, Yoshiharu Kohayakawa, Tomasz Luczak   +2 more
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Decomposition of bounded degree graphs into C4-free subgraphs

We prove that every graph with maximum degree ∆ admits a partition of its edges into O(√∆) parts (as ∆→∞) none of which contains C4 as a subgraph. This bound is sharp up to a constantfactor. Our proof uses an iterated random colouring procedure.Keywords:
Kang, Ross, Perarnau Llobet, Guillem
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Ramsey upper density of infinite graph factors

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József Balogh
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Bounding Monochromatic Triangles Using Squares

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Richard Ehrenborg
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Degree Bipartite Ramsey Numbers

Taiwanese Journal of Mathematics, 2021
Ye Wang
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A note on (t - 1)-chromatic Ramsey number of linear forests

International Journal of Computer Mathematics: Computer Systems Theory, 2020
Amir Khamseh
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The Ramsey number for two graphs of order 5

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Gary Chartrand
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The mixed irredundant Ramsey numberst(3, 7) = 18 andt(3, 8) = 22

Quaestiones Mathematicae, 2014
J H Van Vuuren
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