A linear coloring of a graph G is a proper vertex coloring such that the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc（G） of G is the sm...A linear coloring of a graph G is a proper vertex coloring such that the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc（G） of G is the smallest number of colors in a linear coloring of G. In this paper, we prove that every planar graph G with maximum degree 5 is 11-linear-colorable.展开更多
The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove tha...The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove that TCC holds for planar graph with Δ = 6 and every 7-cycle contains at most two chords.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 11071223)the Natural ScienceFoundation of Zhejiang Province (Grant No. Z6090150)Research Project of Zhejiang Educational Committee(Grant No. Y201121311)
文摘A linear coloring of a graph G is a proper vertex coloring such that the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc（G） of G is the smallest number of colors in a linear coloring of G. In this paper, we prove that every planar graph G with maximum degree 5 is 11-linear-colorable.
文摘The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove that TCC holds for planar graph with Δ = 6 and every 7-cycle contains at most two chords.
