A degree condition for cycles passing through specified vertices and edges. (English) Zbl 1522.05045
Summary: R. Shi [J. Graph Theory 16, No. 3, 267–271 (1992; Zbl 0761.05066)] and B. Bollobás and G. Brightwell [Combinatorica 13, No. 2, 147–155 (1993; Zbl 0780.05033)], independently, obtained a degree sum condition for the existence of a cycle passing through specified vertices. K. A. Berman [Discrete Math. 46, 9–13 (1983; Zbl 0513.05033)] gave a degree sum condition for the existence of a cycle passing through specified edges. In this paper, we obtain a common generalization of these two results.
MSC:
| 05C07 | Vertex degrees |
| 05C45 | Eulerian and Hamiltonian graphs |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
References:
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