Group for Research in Decision Analysis

# Edge Realizability of Connected Simple Graphs

## Gilles Caporossi, Pierre Hansen, and Damir Vukicevic

Necessary and sufficient conditions are provided for existence of a simple graph G, and for a simple and connected graph G' with given numbers mij of edges with end-degrees i,j for $i\leq j\in \left\{ 1,2,\ldots,\Delta \right\}$ where $\Delta$ denotes the maximum degree of G or G'.

, 12 pages