The convex hull of degree sequences of signed graphs

Heather Jordon, Richard McBride, Shailesh Tipnis
2009 Discrete Mathematics  
As shown in [D. Hoffman, H. Jordon, Signed graph factors and degree sequences, J. Graph Theory 52 (2006) 27-36], the degree sequences of signed graphs can be characterized by a system of linear inequalities. The set of all n-tuples satisfying this system of linear inequalities is a polytope P n . In this paper, we show that P n is the convex hull of the set of degree sequences of signed graphs of order n. We also determine many properties of P n , including a characterization of its vertices.
more » ... e convex hull of imbalance sequences of digraphs is also investigated using the characterization given in [D. Mubayi, T.G. Will, D.B. West, Realizing degree imbalances of directed graphs, Discrete Math. 239 (2001) 147-153].
doi:10.1016/j.disc.2008.05.043 fatcat:7gw4jfcibjeqjl5bi5g7ud6mui