Length thresholds for graphic lists given fixed largest and smallest entries and bounded gaps

@article{Barrus2012LengthTF,
  title={Length thresholds for graphic lists given fixed largest and smallest entries and bounded gaps},
  author={Michael D. Barrus and Stephen G. Hartke and Kyle F. Jao and Douglas B. West},
  journal={Discrete Mathematics},
  year={2012},
  volume={312},
  pages={1494-1501}
}
In a list (d1, . . . , dn) of positive integers, let r and s denote the largest and smallest entries. A list is gap-free if each integer between r and s is present. We prove that a gapfree even-summed list is graphic if it has at least r + r+s+1 2s terms. With no restriction on gaps, length at least (r+s+1) 2 4s suffices, as proved by Zverovich and Zverovich. Both bounds are sharp within 1. When the gaps between consecutive terms are bounded by g, we prove a more general length threshold that… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 10 references

Graphs with prescribed degree of vertices (Hungarian)

  • P. Erdős, T. Gallai
  • Mat. Lapok 11
  • 1960
Highly Influential
5 Excerpts

Exercise 1.3.57, Introduction to Graph Theory, 2nd ed., (Prentice-Hall

  • D. B. West
  • 2001
1 Excerpt

Threshold sequences

  • P. L. Hammer, T. Ibaraki, B. Simeone
  • SIAM J. Alg. Disc. Methods 2
  • 1981
1 Excerpt

Graphic sequences and graphic polynomials: a report

  • R. B. Eggleton
  • Infinite and finite sets (Colloq., Keszthely…
  • 1975
1 Excerpt

Graphic sequences with unique realization

  • S.Y.R. Li
  • J. Combinatorial Theory Ser. B 19
  • 1975
1 Excerpt

On the realizability of a set of integers as degrees of the vertices of a graph

  • S. L. Hakimi
  • SIAM J. Appl. Math. 10
  • 1962
2 Excerpts

A remark on the existence of finite graphs

  • V. Havel
  • Casopis Pest. Mat. 80
  • 1955
2 Excerpts

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