Author/Authors :
Borodin، نويسنده , , O.V. and Ivanova، نويسنده , , A.O. and Jensen، نويسنده , , T.R. and Kostochka، نويسنده , , A.V. and Yancey، نويسنده , , M.P.، نويسنده ,
Abstract :
We prove that every normal plane map, as well as every 3-polytope, has a path on three vertices whose degrees are bounded from above by one of the following triplets: ( 3 , 3 , ∞ ) , ( 3 , 4 , 11 ) , ( 3 , 7 , 5 ) , ( 3 , 10 , 4 ) , ( 3 , 15 , 3 ) , ( 4 , 4 , 9 ) , ( 6 , 4 , 8 ) , ( 7 , 4 , 7 ) , and ( 6 , 5 , 6 ) . No parameter of this description can be improved, as shown by appropriate 3-polytopes.
Keywords :
Weight , plane graph , Structural Property , Normal plane map , 3-path
