论文信息 - Split digraphs

Split digraphs

We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to directed graphs, while the second characterization says a digraph is split if and only if its degree sequence satisfies one of the Fulkerson inequalities (which determine when an integer-pair sequence is digraphic) with equality.

Michael Drew Lamar | M. D. Lamar

[1] Peter L. Hammer,et al. The splittance of a graph , 1981, Comb..

[2] Zoltán Toroczkai,et al. A Simple Havel-Hakimi Type Algorithm to Realize Graphical Degree Sequences of Directed Graphs , 2009, Electron. J. Comb..

[3] D. R. Fulkerson. Zero-one matrices with zero trace. , 1960 .

[4] Michael Drew Lamar,et al. Algorithms for realizing degree sequences of directed graphs , 2009, ArXiv.

[5] Florian Roussel,et al. The Strong Perfect Graph Conjecture: 40 years of attempts, and its resolution , 2009, Discret. Math..

[6] Russell Merris,et al. Split graphs , 2003, Eur. J. Comb..

[7] Matthias Müller-Hannemann,et al. Uniform Sampling of Digraphs with a Fixed Degree Sequence , 2010, WG.

[8] N. Mahadev,et al. Threshold graphs and related topics , 1995 .

[9] Sulamita Klein,et al. List Partitions , 2003, SIAM J. Discret. Math..

[10] Regina Tyshkevich,et al. Decomposition of graphical sequences and unigraphs , 2000, Discret. Math..

[11] Michael Drew Lamar. On uniform sampling simple directed graph realizations of degree sequences , 2009, ArXiv.

[12] Daniel J. Kleitman,et al. Algorithms for constructing graphs and digraphs with given valences and factors , 1973, Discret. Math..