On the problem of partitioning into subsets having equal sums
H. Joseph Straight and Paul Schillo
Proc. Amer. Math. Soc. 74 (1979), 229-231
Primary 05C38; Secondary 10A45
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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 path-perfect 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 r-regular path-perfect graph G having p vertices and edges.
Frederick Fink and H.
Joseph Straight, A note on path-perfect graphs, Discrete Math.
33 (1981), no. 1, 95–98. MR 597232
Harary, Graph theory, Addison-Wesley Publishing Co., Reading,
Mass.-Menlo Park, Calif.-London, 1969. MR 0256911
H. J. Straight, Partitions of the vertex set or edge set of a graph, Doctoral Dissertation, Western Michigan University, 1977.
- J. F. Fink and H. J. Straight, Path-perfect graphs, Discrete Math. (to appear). MR 597232 (82a:05077)
- F. Harary, Graph theory, Addison-Wesley, Reading, Mass., 1971. MR 0256911 (41:1566)
- H. J. Straight, Partitions of the vertex set or edge set of a graph, Doctoral Dissertation, Western Michigan University, 1977.
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