Now showing 1 - 10 of 12
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    The tripartite Ramsey numbers rt(C4;2) and rt(C4;3)
    (2014-01-01)
    Buada, S.
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    Longani, V.
    The k-colored tripartite Ramsey numbers r<inf>t</inf>(G; k) is the smallest positive integer n such that any k-coloring of lines of a complete tripartite graph K<inf>n,n,n</inf> there always exists a monochromatic subgraph isomorphic to G. When G is C<inf>4</inf> it is known, but unpublished in a journal, that r<inf>t</inf>(C<inf>4</inf>; 2) = 3. In this paper we simplify the proof of r<inf>t</inf>(C<inf>4</inf>; 2) = 3 and show the new result that r<inf>t</inf>(C<inf>4</inf>; 3) = 7.
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    Periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions
    (2014-01-01)
    Thaiprayoon, Chatthai
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    Tariboon, Jessada
    By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results. © 2014 Chatthai Thaiprayoon et al.
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    An Improved Lower Bound for Bipartite Ramsey Numbers br(2,7) and br(2,8)
    (2017-01-01) ;
    Intarapaiboon, Peerasak
    For complete bipartite graphs Ks,s,Kt,t, the bipartite Ramsey number br(s,t) is the least positive integer b such that if the edges of K<inf>b,b</inf> are colored with red and blue, then there always exists a red Ks,s or a blue Kt,t. We obtain new lower bounds of br(2,7) and br(2,8).
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    Lower bounds of some small bipartite ramsey numbers br(K 2,2 ;k nn, )
    (2017-07-01)
    Adsawatithisakul, Nitiphoom
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    Summart, Waraporn
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    For bipartite graphs G <inf>1</inf> , G <inf>2</inf> , the bipartite Ramsey number br(G <inf>1</inf> ,G <inf>2</inf> ) is the smallest integer b such that any subgraph G of the complete bipartite graph K <inf>bb,</inf> , either G contains a copy of G <inf>1</inf> or its complement relative to K <inf>bb,</inf> contains a copy of G <inf>2</inf> . We obtained lower bounds of br(K <inf>2,2</inf> ;K <inf>nn,</inf> ) for 6≤ n ≤10.
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    Three-point boundary value problems for second-order impulsive integro-differential equations
    (2011-11-21)
    Thaiprayoon, Chatthai
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    Tariboon, Jessada
    In this paper, by using the method of lower and upper solutions coupled with monotone iterative technique, we investigate the existence of extreme solutions of the three-point boundary value problem for secondorder impulsive integro-differential equations. Some comparison results are also formulated.
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    Lower bounds of multicolor bipartite Ramsey numbers br(K p,q;m)
    (2012-10-16)
    The multicolor bipartite Ramsey number br(K <sup>p,q</sup> ;m) is the smallest positive n such that any coloring of the edges of K <sup>n,n</sup> with m-coloring, there are a monochromatic subgraph isomorphic to K <sup>p,q</sup>. In this paper, we show that br(K <sup>p,q</sup>;m) > (p!q!m <sup>p,q-1</sup>) <sup>1/p+q</sup>.
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    A note on the tripartite ramsey numbers rt(C4;2) AND rt(C4;3)
    (2015-01-01)
    Buada, S.
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    Longani, V.
    The k-colored tripartite Ramsey numbers r<inf>t</inf>(G; k) is the smallest positive integer n such that any k-coloring of lines of a complete tripartite graph K<inf>n,n,n</inf> there always exists a monochromatic subgraph isomorphic to G. The values of r<inf>t</inf>(C<inf>4</inf>; 2) = 3, and r<inf>t</inf>(C<inf>4</inf>;3) = 7 are discussed in the article The tripartite Ramsey numbers r<inf>t</inf>(C<inf>4</inf>; 2) and r<inf>t</inf>(C<inf>4</inf>;3) of the Italian Journal of Pure and Applied Mathematics, n. 33-2014. However, there are our technical mistakes on three figures of the article. In this note we correct these mistakes.
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    Multi-point boundary value problem for first order impulsive integro-differential equations with multi-point jump conditions
    (2012-10-01)
    Thaiprayoon, Chatthai
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    Tariboon, Jessada
    In this article we introduce a new definition of impulsive conditions for boundary value problems of first order impulsive integro-differential equations with multi-point boundary conditions. By using the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, we obtain the extremal solutions of the boundary value problem. An example is also discussed to illustrate our results. © 2012 Thaiprayoon et al.
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    Applications of student activity problems for some kirkman type problems
    (2015-12-01)
    Longani, Vites
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    Buada, Sasisophit
    In this paper we apply the ideas from recent works on Student Activity Problems in proposing a theorem on some Kirkman type problems. That is, we find that for any prime number p ≥ 3 it is possible for a school teacher to take p<sup>2</sup> school girls on a walk each day of the p+1 days, walking with p rows of p girls each, in such a way that each pair of girls walk together in the same row on exactly one day.
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    A formula for the number of labelled trees in complete bipartite graph
    (2020-11-24)
    Portawin, Thipapat
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    In this paper, we use Prilfer's construction and exponential generating function to find the formula of the number of labelled tree with r<inf>1</inf>, r<inf>2</inf> end-vertices in complete bipartite graph K<inf>m,n</inf> denoted by L(m, n, r<inf>1</inf>, r<inf>2</inf>). For (equ).