Total coloring of planar graphs without some chordal 6-cycles
نویسندگان
چکیده
A k-total-coloring of a graph G is a coloring of vertex set and edge set using k colors such that no two adjacent or incident elements receive the same color. In this paper, we prove that if G is a planar graph with maximum ∆ ≥ 8 and every 6-cycle of G contains at most one chord or any chordal 6-cycles are not adjacent, then G has a (∆ + 1)-total-coloring.
منابع مشابه
List Edge and List Total Colorings of Planar Graphs without 6-cycles with Chord
Giving a planar graph G, let χl(G) and χ ′′ l (G) denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if a planar graph G without 6-cycles with chord, then χl(G) ≤ ∆(G) + 1 and χ ′′ l (G) ≤ ∆(G) + 2 where ∆(G) ≥ 6.
متن کاملGroup edge choosability of planar graphs without adjacent short cycles
In this paper, we aim to introduce the group version of edge coloring and list edge coloring, and prove that all 2-degenerate graphs along with some planar graphs without adjacent short cycles is group (∆(G) + 1)-edgechoosable while some planar graphs with large girth and maximum degree is group ∆(G)-edge-choosable.
متن کاملSome Results on List Total Colorings of Planar Graphs
Let G be a planar graph with maximum degree Δ. In this paper, it is proved that if Δ ≥ 9, then G is total-(Δ+2)-choosable. Some results on list total coloring of G without cycles of specific lengths are given.
متن کاملThe 3-colorability of planar graphs without cycles of length 4, 6 and 9
In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.
متن کاملAcyclic Colorings and Triangulations of Weakly Chordal Graphs
An acyclic coloring of a graph is a proper vertex coloring without bichromatic cycles. We show that the acyclic colorings of any weakly chordal graph G correspond to the proper colorings of triangulations of G. As a consequence, we obtain polynomial-time algorithms for the acyclic coloring problem and the perfect phylogeny problem on the class of weakly chordal graphs. Our results also imply li...
متن کامل