On the total coloring of planar graphs.
On the total coloring of planar graphs.
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DOI：
10.1515/crll.1989.394.180
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
O. Borodin
中科院分区：
文献类型：
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作者：
O. Borodin
图 G 的总着色是其顶点和边的着色，其中 F(G)u£(G) 的任意两个相邻或关联元素被涂上不同的颜色。 Behzad [1] 和 Vizing [9] 独立推测任何具有最大度 A (G) 的图 G 的总色数 χ, (G) 至多为 A (G) + 2。该猜想被 Vijayaditya [8] 证实为 A (G) = 3，并被 Kostochka [4] 证实为 A (G) ̂ 5。平面图 G 的整个着色是其顶点、边和面以类似方式的着色。 Kronk 和 Mitchem [6] 猜想了束缚 Xe(G) ^ A (G) + 4 并证明了 A (G) = 3。我在 [2] 中证明了：
The total coloring of a graph G is a coloring of its vertices and edges in which any two adjacent or incident elements of F(G)u£(G) are colored with different colors. Behzad [1] and Vizing [9] conjectured independently that the total chromatic number χ, (G) of any graph G with the maximum degree A (G) is at most A (G) + 2. This conjecture was confirmed for A (G) = 3 by Vijayaditya [8] and for A (G) ̂ 5 by Kostochka [4]. The entire coloring of a planar graph G is a coloring of its vertices, edges and faces in a similar fashion. Kronk and Mitchem [6] conjectured the bound Xe(G) ^ A (G) + 4 and proved it for A (G) = 3. I proved in [2] :