Generalized Ramsey theory for graphs. II. Small diagonal numbers
Authors:
Václav Chvátal and Frank Harary
Journal:
Proc. Amer. Math. Soc. 32 (1972), 389394
MSC:
Primary 05C35
MathSciNet review:
0332559
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Consider a finite nonnull graph G with no loops or multiple edges and no isolated points. Its Ramsey number is defined as the minimum number p such that every 2coloring of the lines of the complete graph must contain a monochromatic G. This generalizes the classical diagonal Ramsey numbers . We obtain the exact value of the Ramsey number of every such graph with at most four points.
 [1]
V. Chvátal and F. Harary, Generalized Ramsey theory for graphs. I: Diagonal numbers, Period. Math. (to appear).
 [2]
Václav
Chvátal and Frank
Harary, Generalized Ramsey theory for graphs. III. Small
offdiagonal numbers, Pacific J. Math. 41 (1972),
335–345. MR 0314696
(47 #3248)
 [3]
A.
W. Goodman, On sets of acquaintances and strangers at any
party, Amer. Math. Monthly 66 (1959), 778–783.
MR
0107610 (21 #6335)
 [4]
R.
E. Greenwood and A.
M. Gleason, Combinatorial relations and chromatic graphs,
Canad. J. Math. 7 (1955), 1–7. MR 0067467
(16,733g)
 [5]
Frank
Harary, Graph theory, AddisonWesley Publishing Co., Reading,
Mass.Menlo Park, Calif.London, 1969. MR 0256911
(41 #1566)
 [6]
Frank
Harary, The twotriangle case of the aquaintance graph, Math.
Mag. 45 (1972), 130–135. MR 0295962
(45 #5023)
 [1]
 V. Chvátal and F. Harary, Generalized Ramsey theory for graphs. I: Diagonal numbers, Period. Math. (to appear).
 [2]
 , Generalized Ramsey theory for graphs. III: Small offdiagonal numbers, Pacific J. Math. (to appear). MR 0314696 (47:3248)
 [3]
 A. W. Goodman, On sets of acquaintances and strangers at any party, Amer. Math. Monthly 66 (1959), 778783. MR 21 #6335. MR 0107610 (21:6335)
 [4]
 R. E. Greenwood and A. M. Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math. 7 (1955), 17. MR 16, 733. MR 0067467 (16:733g)
 [5]
 F. Harary, Graph theory, AddisonWesley, Reading, Mass., 1969. MR 41 #1566. MR 0256911 (41:1566)
 [6]
 , The twotriangle case of the acquaintance graph, Math. Mag. (to appear). MR 0295962 (45:5023)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
05C35
Retrieve articles in all journals
with MSC:
05C35
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919720332559X
PII:
S 00029939(1972)0332559X
Article copyright:
© Copyright 1972
American Mathematical Society
