3-正则Halin图的全色数

On Total Chromatic Number of Halin Graphs with Δ(G)=3

研究了△ (G) =3时Halin图的全色数 ,证明了 :(i)对于 3-正则的Halin图G ,有 4 ≤xT(G) ≤ 5;(ii)若将 3-正则Halin图每边剖分一次 ,则对于剖分图M 有xT(M ) =4 ,这里△ (G)表示图G的最大度数 ,xT(G)表示图G的全色数。

In this paper ,we obtained some results abo ut x_T(G) for Halin graphs with (Δ(G)=3),and proved that: (i) 4≤ x_T(G)≤5; (ii) x_T(H)=4 where H is a graph obtained by subdivid ing every edge of G once a time, where x_T(G) denotes the total chromat ic number of G, and Δ(G) the maximum degree of G.