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On Ramsey (4K2, P3)-minimal graphs
(AKCE International Journal of Graphs and Combinatorics, 2018-08-13)
Let F, G, and H be simple graphs. We write F → (G, H) to mean that any red–blue coloring of all edges of F will contain
either a red copy of G or a blue copy of H. A graph F (without isolated vertices) satisfying F → (G, ...
Subdivision of graphs in R(mK2,P4)
(Heliyon, 2020-06-12)
For any graphs 𝐹 ,𝐺, and 𝐻, the notation 𝐹 → (𝐺,𝐻) means that any red-blue coloring of all edges of 𝐹 will
contain either a red copy of 𝐺 or a blue copy of 𝐻. The set (𝐺,𝐻) consists of all Ramsey (𝐺,𝐻)-minimal ...
On Ramsey Minimal Graphs for a 3-Matching Versus a Path on Five Vertices
(Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation, 2022-02-08)
Let 𝐺, 𝐻, and 𝐹 be simple graphs. The notation 𝐹 ⟶ (𝐺, 𝐻) means that any red-blue coloring of all edges of 𝐹 contains
a red copy of 𝐺 or a blue copy of 𝐻. The graph 𝐹 satisfying this property is called a Ramsey ...
On Ramsey (mK2, H)-Minimal Graphs
(Graphs and Combinatorics, 2017-01-02)
Let R(G, H) denote the set of all graphs F satisfying F → (G, H) and
for every e ∈ E(F), (F − e) (G, H). In this paper, we derive the necessary and
sufficient conditions for graphs belonging to R(mK2, H) for any graph ...
All unicyclic Ramsey (mK2, P4)-minimal graphs
(The Australasian Journal of Combinatorics, 2022-02-01)
For graphs F, G and H, we write F → (G, H) to mean that if the edges
of F are colored with two colors, say red and blue, then the red subgraph
contains a copy of G or the blue subgraph contains a copy of H. The
graph F ...
Subdivision of Graphs in R(mK2,P4)
(Heliyon, 2020-04-20)
For any graphs 𝐹 ,𝐺, and 𝐻, the notation 𝐹 → (𝐺,𝐻) means that any red-blue coloring of all edges of 𝐹 will contain either a red copy of 𝐺 or a blue copy of 𝐻. The set (𝐺,𝐻) consists of all Ramsey (𝐺,𝐻)-minimal ...