On the problem of partitioning into subsets having equal sums

Authors:
H. Joseph Straight and Paul Schillo

Journal:
Proc. Amer. Math. Soc. **74** (1979), 229-231

MSC:
Primary 05C38; Secondary 10A45

DOI:
https://doi.org/10.1090/S0002-9939-1979-0524291-0

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 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.

**[1]**John Frederick Fink and H. Joseph Straight,*A note on path-perfect graphs*, Discrete Math.**33**(1981), no. 1, 95–98. MR**597232**, https://doi.org/10.1016/0012-365X(81)90262-4**[2]**Frank Harary,*Graph theory*, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London, 1969. MR**0256911****[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:
https://doi.org/10.1090/S0002-9939-1979-0524291-0

Article copyright:
© Copyright 1979
American Mathematical Society