Abstract
Let G be a connected graph of order n and girth g. If d G (u) + d G (v) ≥ n − 2g + 5 for any two non-adjacent vertices u and v, then G is up-embeddable. Further more, the lower bound is best possible. Similarly the result of k-edge connected simple graph with girth g is also obtained, k = 2,3.
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Partially supported by the Postdoctoral Seience Foundation of Central South University and NNSFC under Grant No. 10751013.
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Chen, Y., Liu, Y. Up-Embeddability of a Graph by Order and Girth. Graphs and Combinatorics 23, 521–527 (2007). https://doi.org/10.1007/s00373-007-0746-8
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DOI: https://doi.org/10.1007/s00373-007-0746-8