A Note On Reed's Conjecture

In [5], Reed conjectures that every graph satisfies ++1 2 . We prove this holds for graphs with disconnected complement. Combining this fact with a result of Molloy proves the conjecture for graphs satisfying > n 2 . Generalizing this we prove that the conjecture holds for graphs satisfying > n+32 . It follows that the conjecture holds for graphs satisfying n + 2 - + n + 5 - . In the final section, we show that if G is an even order counterexample to Reed's conjecture, then G has a 1-factor.

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: Landon Rabern
• Keywords: Conjecture, Generalizing, Graph Satisfies, SIAMDM 2008