Corpus ID: 119591566

A Summary of Problems and Results related to the Caccetta-Haggkvist Conjecture

@article{Sullivan2006ASO,
  title={A Summary of Problems and Results related to the Caccetta-Haggkvist Conjecture},
  author={B. Sullivan},
  journal={arXiv: Combinatorics},
  year={2006}
}
  • B. Sullivan
  • Published 2006
  • Mathematics
  • arXiv: Combinatorics
  • This paper is an attempt to survey the current state of our knowledge on the Caccetta-Haggkvist conjecture and related questions. In January 2006 there was a workshop hosted by the American Institute of Mathematics in Palo Alto, on the Caccetta-Haggkvist conjecture, and this paper partly originated there, as a summary of the open problems and partial results presented at the workshop. This summary includes results and open problems related to Caccetta-Haggkvist, Seymour's Second Neighborhood… CONTINUE READING
    19 Citations
    On the Caccetta-Häggkvist Conjecture with a Forbidden Transitive Tournament
    • A. Grzesik
    • Mathematics, Computer Science
    • Electron. J. Comb.
    • 2017
    • 3
    Total domination and the Caccetta-Häggkvist conjecture
    • 1
    • PDF
    Substructures in digraphs
    • PDF
    Seymour's Second Neighborhood Conjecture for Subsets of Vertices
    • 1
    • PDF
    On the Number of Vertex-Disjoint Cycles in Digraphs
    • PDF
    Embedding cycles of given length in oriented graphs
    • 3
    • PDF
    Extremal Problems in Digraphs
    • 9
    • PDF
    Short Directed Cycles in Bipartite Digraphs
    • PDF
    Short rainbow cycles in graphs and matroids
    • 1
    • PDF

    References

    SHOWING 1-10 OF 24 REFERENCES
    A note on short cycles in diagraphs
    • 43
    • Highly Influential
    • PDF
    On the girth of digraphs
    • Jian Shen
    • Mathematics, Computer Science
    • Discret. Math.
    • 2000
    • 34
    • Highly Influential
    • PDF
    Short cycles in digraphs
    • 28
    • Highly Influential
    Even Cycles in Directed Graphs
    • 60
    • Highly Influential
    An Application of Connectivity Theory in Graphs to Factorizations of Elements in Groups
    • 57
    • Highly Influential
    Median orders of tournaments: A tool for the second neighborhood problem and Sumner's conjecture
    • 45
    • Highly Influential
    A note on minimal directed graphs with given girth
    • 40
    • Highly Influential
    Squaring a tournament: a proof of Dean's conjecture
    • 13
    Short Cycles in Digraphs with Local Average Outdegree at Least Two
    • Jian Shen
    • Computer Science, Mathematics
    • Electron. J. Comb.
    • 2003
    • 3
    • Highly Influential
    • PDF
    Directed Triangles in Digraphs
    • Jian Shen
    • Mathematics, Computer Science
    • J. Comb. Theory, Ser. B
    • 1998
    • 25
    • Highly Influential
    • PDF