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    Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory

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    Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory.pdf (2.784Mb)
    Date
    2020
    Author
    Badawi, Ayman
    Rissner, Roswitha
    Advisor(s)
    Unknown advisor
    Type
    Peer-Reviewed
    Article
    Published version
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    Abstract
    For a partially ordered set(A, ≤), letGA be the simple, undirected graph with vertex set A such that two vertices a ≠ ∈ b A are adjacent if either a ≤ b or b a ≤ . We call GA the partial order graph or comparability graph of A. Furthermore, we say that a graph G is a partial order graph if there exists a partially ordered set A such that G = GA. For a class of simple, undirected graphs and n, m ≥ 1, we define the Ramsey number (n m, ) with respect to to be the minimal number of vertices r such that every induced subgraph of an arbitrary graph in consisting of r vertices contains either a complete n-clique Kn or an independent set consisting of m vertices. In this paper, we determine the Ramsey number with respect to some classes of partial order graphs. Furthermore, some implications of Ramsey numbers in ring theory are discussed.
    DSpace URI
    http://hdl.handle.net/11073/21411
    External URI
    https://doi.org/10.1515/math-2020-0085
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