## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 21, Number 2 (1991), 351-383.

### An algorithm for constructing a weight-controlled subset and its application to graph coloring problem

**Full-text: Open access**

#### Article information

**Source**

Hiroshima Math. J., Volume 21, Number 2 (1991), 351-383.

**Dates**

First available in Project Euclid: 21 March 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1206130972

**Digital Object Identifier**

doi:10.32917/hmj/1206130972

**Mathematical Reviews number (MathSciNet)**

MR1098823

**Zentralblatt MATH identifier**

0737.05070

**Subjects**

Primary: 05A05: Permutations, words, matrices

Secondary: 05C15: Coloring of graphs and hypergraphs 05C85: Graph algorithms [See also 68R10, 68W05]

#### Citation

Kitagawa, Fumio. An algorithm for constructing a weight-controlled subset and its application to graph coloring problem. Hiroshima Math. J. 21 (1991), no. 2, 351--383. doi:10.32917/hmj/1206130972. https://projecteuclid.org/euclid.hmj/1206130972

#### References

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- [2] K. Appel and W.Haken, Every planar map is four colorable, Illinois J. of Math., 21 (3) (1977).Zentralblatt MATH: 0387.05009
- [3] J. S. Appleby, D. V. Blake and E. A. Newman, Techniques for producing school timetables on a computer and their application to other scheduling problems, Comp. J., 3 (5) (1961) 237-245.
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- [5] A. J. Cole, The preparation of examination timetables using a small-store computer, Comp. J., 7 (1964) 117-121.Zentralblatt MATH: 0123.13206
- [6] J. Csima and C. C. Gotlieb, Tests on a computer method for constructing school timetables, Comm. ACM, 7 (3) (1964) 160-163.Zentralblatt MATH: 0121.12209
- [7] M. A. H. Dempster, Two algorithms for the timetable problem, Combinatorial Theory and its Applications (Academic Press, London, 1971) 63-85.
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- [10] C. C. Gotlieb, The construction of class-teacher timetables, Proc. IFIP Congr. Munich (North Holland, Amsterdam, 1962) 73-77.Zentralblatt MATH: 0143.18802
- [11] H. Ikeda, S. Itoh and S. Yamamoto, An algorithm for school timetable construction, Proceedings of the 15th Conf. on Information Processing Society of Japan (IPSJ) (1974) 553-554 (Japanese).
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- [14] F. Kitagawa and H. Ikeda, An existential problem of 0-1 matrix and its application to school timetable construction, 29th IPSJ (1984) 1807-1808 (Japanese).
- [15] F. Kitagawa and H. Ikeda, A model of timetable which includes many complex conditions, 32nd IPSJ (1986) 2131-2132 (Japanese).
- [16] F. Kitagawa and H. Ikeda, An existential problem of a weight-controlled subset and its application to school time-table construction, Discrete math. 72 (1988) 195-211.
- [17] J. Lions, Matrix reduction using the Hungarian method for the generation of school timetables, Comm. ACM, 9 (5) (1966) 349-354.Zentralblatt MATH: 0171.15307
- [18] J. Lions, A counter-example for Gotlieb's method for the construction of school timetables, Comm. ACM, 9 (1966) 697-698.
- [19] J. Lions, The Ontario school scheduling program, Comp. J., 10 (1967) 14-20.
- [20] G. A. Neufeld and J. Tarter, Graph colouring condition for the existence of solutions to the timetable problem, Comm. ACM, 17 (8) (1974) 450-453.
- [21] K. Ohmori, Latin square, (Toyamabo 1973) (Japanese).
- [22] A. Salazar and R. V. Oakford, A graph formulation of a school scheduling algorithm, Comm. ACM, 17 (12) (1974) 696-698.
- [23] D. J. A. Welsh and M. B. Powell, An upper bound to the chromatic number of a graph and its application to timetabling problems, Comp. J., 10 (1) (1967) 85-86.Zentralblatt MATH: 0147.15206
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- [25] S. Yamamoto, H. Ikeda, S. Sge-eda, K. Ushio and N. Hamada, On Claw-decomposition of complete graphs and cmplete bi-graphs, Hiroshima Math. J., 5 (1975) 33-42.
- [26] A. P. Yule, Extensions to the heuristic algorithm for university timetables, Comp. J., 10 (1967) 360-364.

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