## Characterization of magic graphs.(English)Zbl 0571.05030

The following is proved: A graph $$G$$ is magic iff every edge of $$G$$ belongs to a (1- 2)-factor and every couple of edges is separated by a (1-2)-factor. By (1-2)-factor we mean such factor of $$G$$ if each of its components is a regular graph of degree 1 or 2.
Reviewer: J. Fiamčík

### MSC:

 05C35 Extremal problems in graph theory

### Keywords:

magic graphs; (1-2)-factor
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### References:

 [1] M. Doob: Characterizations of Regular Magic Graphs. J. Combinatorial Theory, Ser. B, 25, 94-104 (1978). · Zbl 0384.05054 [2] J. Mühlbacher: Magische Quadrate und ihre Verallgemeinerung: ein graphentheoretisches Problem, Graph, Data Structures, Algorithms. Hansen Verlag 1979, München. · Zbl 0407.05077 [3] J. Sedláček: Problem 27, in ”Theory of Graphs and Its Applications”. Proc. Symp. Smolenice 1963, 163-167. [4] J. Sedláček: On magic graphs. Math. Slov. 26 (1976), 329-335. [5] B. M. Stewart: Magic Graphs. Canad. J. Math., 18 (1966), 1031-1059. · Zbl 0149.21401
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