Results 81 to 90 of about 1,045 (103)

Generalized Ramsey theory for graphs IV, the Ramsey multiplicity of a graph

Networks, 1974
AbstractA Proper graph G has no isolated points. Its Ramsey number r(G) is the minimum p such that every 2‐coloring of the edges of Kp contains a monochromatic G. The Ramsey multiplicity R(G) is the minimum number of monochromatic G in any 2‐coloring of Kr(G). With just one exception, namely K4, we determine R(G) for proper graphs with at most 4 points.
Frank Harary, Geert C. E. Prins
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A generalization of Ramsey theory for linear forests

International Journal of Computer Mathematics, 2012
Chung and Liu defined the d - chromatic Ramsey numbers as a generalization of Ramsey numbers by replacing the usual condition with a slightly weaker condition. Let 1 d c and let . Assume A 1, A 2,..., A t are all d -subsets of a set containing c distinct colours. Let G 1, G 2,..., G t be graphs.
Amir Khamseh, G. R. Omidi
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Generalized ramsey theory for graphs VII: Ramsey numbers for multigraphs and networks

Networks, 1978
AbstractRamsey problems are examined for the different varieties of graphs and digraphs, with and without loops and multiple edges, and even for networks. In every case, the resulting Ramsey number either fails to exist, or has a trivial value, or equals the value for the underlying graph or digraph.
Frank Harary, Allen J. Schwenk
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On bipartite generalized Ramsey theory

Ars Comb., 2003
Summary: Given graphs \(G\) and \(H\), an edge coloring of \(G\) is an \((H,q)\)-coloring if the edges of every copy of \(H \subset G\) together receive at least \(q\) colors. Let \(r(G,H,q)\) denote the minimum number of colors in a \((H,q)\)-coloring of \(G\). The authors study the behaviour of \(r(K_{n,n},K_{p,p},q)\), namely for those values of \(q\
Gábor N. Sárközy, Stanley M. Selkow
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Generalized ramsey theory VIII. The size ramsey number of small graphs

1983
The ramsey number r(F) of a graph F with no isolates has been much studied. We now investigate its size Ramsey number ζ(F) defined as the minimum q such that there exists a graph G with q edges for which every 2-coloring of E(G) has a monochromatic F.
Frank Harary, Zevi Miller
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Sraffa’s Conceptualization of Own Rates Is Based only on Probabilistic Price Expectations because Sraffa Accepted Ramsey’s Definition that Confidence Is Measured by Subjective Probability Alone: Keynes’s Liquidity Preference Function in the General Theory Has Nothing to Do with Probability, but Is An Inverse Function of the Evidential Weight of the Argument, Where Uncertainty Is also Defined as An Inverse Function of the Evidential Weight of the Argument

SSRN Electronic Journal, 2021
Sraffa made a number of margin notes in chapter 17 in his copy of the General Theory .Contrary to Joan Robinson’s 1978 claim ,that Sraffa had uncovered logical and mathematical errors in Keynes’s liquidity preference theory of the rate of interest when he generalized his theory in chapter 17,the margin notes made by Sraffa are all erroneous . Sraffa’
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Ramsey theory for a generalized fan versus triangles

Utilitas Mathematica
<p>In this paper, we consider Ramsey and Gallai-Ramsey numbers for a generalized fan <span class="math inline">\(F_{t,n}:=K_1+nK_t\)</span> versus triangles. Besides providing some general lower bounds, our main results include the evaluations of <span class="math inline">\(r(F_{3,2}, K_3)=13\)</span> and <span class ...
Mark Budden, Richard Prange
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Generalized ramsey theory for graphs - a survey

1974
Almost nonexistent a few years ago, the field of generalized Ramsey theory for graphs is now being pursued very actively and with remarkable success. This survey paper will emphasize the following class of problems: Given graphs G1, ..., Gc, determine or estimate the Ramsey number r(G1, ..., Gc), the smallest number p such that if the lines of a ...
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Generalized ramsey theory XV: Achievement and avoidance games for bipartite graphs

1984
Let two opponents, Oh and Ex, play the following game on the complete bipartite graph Kn,n. Oh colors one of the edges green and Ex colors a different edge red, and so on. The goal of each player is to be the first one to construct in his own color a predetermined bipartite graph M with no isolated points.
Martin Erickson, Frank Harary
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Generalized Ramsey Numbers Involving Subdivision Graphs, And Related Problems in Graph Theory

1980
Publisher Summary This chapter discusses generalized Ramsey numbers involving subdivision graphs and related problems in graph theory. It is assumed that if G1 and G2 are (simple) graphs, then the Ramsey number r(G1, G2) is the smallest integer n such that if one colors the complete graph Kn in two colors I and II, then either color I contains G1 as ...
S.A. Burr, P. Erdös
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