Unicyclic Ramsey (P3, Pn)-minimal graphs obtained from trees in the same class

If G, H and F are finite and simple graphs, notation F → (G, H) means that for any red-blue coloring of the edges of F, there is either a red subgraph isomorphic to G or a blue subgraph isomorphic to H. A graph F is a Ramsey (G, H)-minimal graph if F → (G, H) and for every e ∈ E(F), graph F − e ↛ (G...

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Bibliographic Details
Published in:Journal of physics. Conference series 2020-05, Vol.1538 (1), p.12016
Main Authors: Rahmadani, D, Assiyatun, H, Baskoro, E T
Format: Article
Language:English
Subjects:
Graph theory
Graphs
Isomorphism
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Summary:If G, H and F are finite and simple graphs, notation F → (G, H) means that for any red-blue coloring of the edges of F, there is either a red subgraph isomorphic to G or a blue subgraph isomorphic to H. A graph F is a Ramsey (G, H)-minimal graph if F → (G, H) and for every e ∈ E(F), graph F − e ↛ (G, H). The class of all Ramsey (G, H)-minimal graphs (up to isomorphism) will be denoted by R(G, H). The characterization of all graphs in the infinite class R(P3, Pn) is still open, for any n ≥ 4. In this paper, we find an infinite families of trees in R(P3, P5). We determine how to construct unicyclic graphs in R(P3, Pn), for any n ≥ 5 from trees in the same class. Further, we give some properties for the unicyclic graphs constructed from trees in R(P3, Pn), for any n ≥ 5.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1538/1/012016