broken line graphs questions 001

Báo cáo toán học: "A strengthening of Brooks’ Theorem for line graphs" doc

Báo cáo toán học:
... counterexamples that are the line graph of a multigraph for ∆(G) ≥ This is tight since the above counterexample for ∆(G) = is a line graph of a multigraph Theorem If G is the line graph of a multigraph with ... χ(G) ≤ ω(G)+∆(G)+1 holds for all graphs G For further information about Reed’s conjecture, see King’s thesis [11] and King and Reed’s proof of the conjecture for quasi -line graphs [13] Back in ... ω(G) the electronic journal of combinatorics 18 (2011), #p145 Proof of Theorem Suppose the theorem is false and choose a counterexample F minimizing ∆(F ) By Brooks’ Theorem we must have χ(F )...
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