Open AccessUnicyclic Ramsey (P 3, Pn )-minimal graphs obtained from trees in the same class
Author(s) -
Desi Rahmadani,
Hilda Assiyatun,
Edy Tri Baskoro
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1538/1/012016
Subject(s) - combinatorics , mathematics , induced subgraph , graph , induced subgraph isomorphism problem , ramsey's theorem , discrete mathematics , line graph , voltage graph , vertex (graph theory)
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 ( P 3 , P n ) is still open, for any n ≥ 4. In this paper, we find an infinite families of trees in R ( P 3 , P 5 ). We determine how to construct unicyclic graphs in R ( P 3 , P n ), for any n ≥ 5 from trees in the same class. Further, we give some properties for the unicyclic graphs constructed from trees in R ( P 3 , P n ), for any n ≥ 5.