• Corpus ID: 3105086

A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences

@article{Cairns2014ASR,
  title={A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences},
  author={Grant Cairns and Stacey Mendan and Yury Nikolayevsky},
  journal={Australas. J Comb.},
  year={2014},
  volume={60},
  pages={217-226}
}
We give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a sufficient condition for a finite sequence of positive integers to be the vertex degree list of both parts of a bipartite graph. The condition depends only on the length of the sequence and its largest and smallest elements. 

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References

SHOWING 1-9 OF 9 REFERENCES

An improvement of a result of Zverovich - Zverovich

We give an improvement of a result of Zverovich and Zverovich which gives a condition on the first and last elements in a decreasing sequence of positive integers for the sequence to be graphic, that

Contributions to the theory of graphic sequences

Reduced criteria for degree sequences

Degree Sequences for Graphs with Loops

This paper considers graphs, without multiple edges, in which there is at most one loop at each vertex. We give Erdos--Gallai type theorems for such graphs and we show how they relate to bipartite

Symmetric Bipartite Graphs and Graphs with Loops

We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an

A note on regular Ramsey graphs

It is proved that there is an absolute constant C>0 so that for every natural $n$ there exists a triangle-free graph with no independent set of size at least C\sqrt{n\log n}$.

Combinatorial Properties of Matrices of Zeros and Ones

  • H. Ryser
  • Mathematics
    Canadian Journal of Mathematics
  • 1957
This paper is concerned with a matrix A of m rows and n columns, all of whose entries are 0's and l's. Let the sum of row i of A be denoted by r i (i = 1, … , m) and let the sum of column i of A be

A theorem on flows in networks

The theorem to be proved in this note is a generalization of a well-known combinatorial theorem of P. Hall, [4].