کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4647926 | 1342383 | 2012 | 5 صفحه PDF | دانلود رایگان |
Let GG be a planar graph with maximum degree Δ(G)Δ(G). In this paper, we prove that GGis (Δ(G)+1Δ(G)+1)-total choosable if GG has no cycle of length from 44 to kk and has minimum distance at least dΔdΔ between triangles for (Δ(G),k,dΔ)=(6,4,1),(5,5,2),(5,6,1),(5,7,0),(4,6,3)(Δ(G),k,dΔ)=(6,4,1),(5,5,2),(5,6,1),(5,7,0),(4,6,3), (4,7,2),(4,10,1)(4,7,2),(4,10,1).
► We study (D+1)(D+1)-total choosability of planar graphs with maximum degree DD.
► The absence of cycle of length from 4 to kk and of triangles at distance less than dd is sufficient.
► The cases (D,k,d)=(6,4,1),(5,5,2),(5,6,1),(5,7,0),(4,6,3),(4,7,2),(4,10,1)(D,k,d)=(6,4,1),(5,5,2),(5,6,1),(5,7,0),(4,6,3),(4,7,2),(4,10,1) are proved.
► These results improve and generalize recent results from Borodin et al., Chang et al., and Hou et al.
► The proofs rely on the structural properties of an hypothetical minimal counter example.
Journal: Discrete Mathematics - Volume 312, Issue 14, 28 July 2012, Pages 2126–2130