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In [5], Reed conjectures that every graph satisfies χ ≤ ⌈ω+∆+1 2 ⌉ . We prove this holds for graphs with disconnected complement. Combining this fact with a result of Molloy proves the conjecture for(More)
It is shown that any graph with maximum degree ∆ in which the average degree of the induced subgraph on the set of all neighbors of any vertex exceeds 6k 2 6k2+1 ∆ + k+ 6 is either (∆ − k)-colorable(More)
We introduce a notion of vertex association and consider sequences of these associations. This allows for slick proofs of a few known theorems as well as showing that for any induced subgraph H of G,(More)