The edge-face chromatic number Xef （G） of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, t...The edge-face chromatic number Xef （G） of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, the authors prove that every 2-connected plane graph G with △（G）≥｜G｜ - 2≥9 has Xef（G） = △（G）.展开更多
Wang Wei-fan[1] proved that the edge-face chromatic number of a 2-connected 1-tree with the maximum degree is not less than 6 is its maximum degree, and he conjectured that it is true when the maximum degree is 5. Thi...Wang Wei-fan[1] proved that the edge-face chromatic number of a 2-connected 1-tree with the maximum degree is not less than 6 is its maximum degree, and he conjectured that it is true when the maximum degree is 5. This paper proves the conjecture.展开更多
Definition 1. Assume that G（V, E, F）is a 3-connected plane graph. Remove all edges on the boundary of a face f<sub>0</sub> whose degree of all vertices of $ V（f-0）$ is 3 such that G becomes a tree T wh...Definition 1. Assume that G（V, E, F）is a 3-connected plane graph. Remove all edges on the boundary of a face f<sub>0</sub> whose degree of all vertices of $ V（f-0）$ is 3 such that G becomes a tree T whose degree of all vertices except those of V（f<sub>0</sub>） is at least 3. Then G is called a Halin-graph, f<sub>0</sub>展开更多
基金This research is supported by NNSF of China(40301037, 10471131)
文摘The edge-face chromatic number Xef （G） of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, the authors prove that every 2-connected plane graph G with △（G）≥｜G｜ - 2≥9 has Xef（G） = △（G）.
文摘Wang Wei-fan[1] proved that the edge-face chromatic number of a 2-connected 1-tree with the maximum degree is not less than 6 is its maximum degree, and he conjectured that it is true when the maximum degree is 5. This paper proves the conjecture.
文摘Definition 1. Assume that G（V, E, F）is a 3-connected plane graph. Remove all edges on the boundary of a face f<sub>0</sub> whose degree of all vertices of $ V（f-0）$ is 3 such that G becomes a tree T whose degree of all vertices except those of V（f<sub>0</sub>） is at least 3. Then G is called a Halin-graph, f<sub>0</sub>
