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Graphic Sequences with an A-Connected Realization

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Abstract

A non-increasing sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) of non-negative integers is said to be graphic if it is the degree sequence of a simple graph G on n vertices. Let A be an (additive) abelian group. An extremal problem for a graphic sequence to have an A-connected realization is considered as follows: determine the smallest even integer \({\sigma (A, n)}\) such that each graphic sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) with d n ≥ 2 and \({\sigma (\pi) = d_1 + d_2 + \cdots +d_n \ge \sigma (A, n)}\) has an A-connected realization. In this paper, we determine \({\sigma (A, n)}\) for |A| ≥ 5 and n ≥ 3.

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References

  1. Bondy J.A., Murty U.S.R.: Graph Theory with Applications. American Elsevier, New York (1976)

    MATH  Google Scholar 

  2. Jaeger F.: Nowhere-zero flow problems. In: Beineke, L.W., Wilson, R.J. (eds) Topics in Graph Theory, vol. 3, pp. 70–95. Academic Press, London (1988)

    Google Scholar 

  3. Jaeger F., Linial N., Payan C., Tarsi M.: Group connectivity of graphs–A nonhomogeneous analogue of nowhere zero flow properties. J. Comb. Theory Ser. B. 56, 165–182 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kleitman D.J., Wang D.L.: Algorithm for constructing graphs and digraphs with given valences and factors. Discrete Math. 6, 79–88 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lai H.J.: Group connectivity of 3-edge-connected chordal graphs. Graphs Comb. 16, 165–176 (2000)

    Article  MATH  Google Scholar 

  6. Lai H.J., Li X.W., Shao Y.H., Zhan M.Q.: Group connectivity and group colorings of graphs—a survey. Acta Mathematica Sinica, English Series. 27, 405–434 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Luo R., Xu R., Yu G.X.: An extremal problem on group connectivity of graphs. Eur. J. Comb. 33, 1078–1085 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Luo R., Xu R., Zang W.A., Zhang C.Q.: Realizing degree sequences with graphs having nowhere-zero 3-flows. SIAM J. Discrete Math. 22, 500–519 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Luo R., Zang W.A., Zhang C.Q.: Nowhere-zero 4-flows, simultaneous edge-colorings, and critical partial Latin squares. Combinatorica 24, 641–657 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yin J.H., Guo G.D.: The smallest degree sum that yields graphic sequences with a Z 3-connected realization. Eur. J. Comb. 34, 806–811 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, China

    Jianhua Yin

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26506-6310, USA

    Rong Luo

  3. Lane Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, WV, 26506, USA

    Guodong Guo

Authors
  1. Jianhua Yin
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  2. Rong Luo
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  3. Guodong Guo
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Corresponding author

Correspondence to Jianhua Yin.

Additional information

J. Yin’s research is partially supported by National Natural Science Foundation of China (Grant No. 11161016).

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Yin, J., Luo, R. & Guo, G. Graphic Sequences with an A-Connected Realization. Graphs and Combinatorics 30, 1615–1620 (2014). https://doi.org/10.1007/s00373-013-1363-3

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  • DOI: https://doi.org/10.1007/s00373-013-1363-3

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