On the problem of partitioning into subsets having equal sums
Authors:
H. Joseph Straight and Paul Schillo
Journal:
Proc. Amer. Math. Soc. 74 (1979), 229231
MSC:
Primary 05C38; Secondary 10A45
MathSciNet review:
524291
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Abstract: Let N denote the set of natural numbers and let . For S a finite subset of N, let denote the sum of the elements in S. Then . Suppose , where s and t are integers and . We show that can be partitioned into such that , for . Such a partition is called an (s, t)partition of . A graph G having edges is said to be pathperfect if the edge set of G can be partitioned as so that induces a path of length i, for . Suppose p and n are positive integers and r is an even positive integer with and . The existence of an (r/2, p)partition of is used to show the existence of an rregular pathperfect graph G having p vertices and edges.
 [1]
John
Frederick Fink and H.
Joseph Straight, A note on pathperfect graphs, Discrete Math.
33 (1981), no. 1, 95–98. MR 597232
(82a:05077), http://dx.doi.org/10.1016/0012365X(81)902624
 [2]
Frank
Harary, Graph theory, AddisonWesley Publishing Co., Reading,
Mass.Menlo Park, Calif.London, 1969. MR 0256911
(41 #1566)
 [3]
H. J. Straight, Partitions of the vertex set or edge set of a graph, Doctoral Dissertation, Western Michigan University, 1977.
 [1]
 J. F. Fink and H. J. Straight, Pathperfect graphs, Discrete Math. (to appear). MR 597232 (82a:05077)
 [2]
 F. Harary, Graph theory, AddisonWesley, Reading, Mass., 1971. MR 0256911 (41:1566)
 [3]
 H. J. Straight, Partitions of the vertex set or edge set of a graph, Doctoral Dissertation, Western Michigan University, 1977.
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DOI:
http://dx.doi.org/10.1090/S00029939197905242910
PII:
S 00029939(1979)05242910
Article copyright:
© Copyright 1979 American Mathematical Society
