2006/09/27 by Baogang Xu, Xu, Baogang, Qinglin Yu +1
Computer Science · Mathematics · Neuroscience · #05C15 #05C78 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Nuclear Receptors and Signaling #math.CO #msc:05C15 #msc:05C78
paper · pdf · doi:10.48550/arxiv.math/0609757
7 pages
arxiv created 2006/09/27 · openalex publication_date 2006/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An (L,d)^*-coloring is a mapping ϕ that assigns a color ϕ(v)∈ L(v) to each vertex v∈ V(G) such that at most d neighbors of v receive colore ϕ(v). A graph is called (m,d)^*-choosable, if G admits an (L,d)^*-coloring for every list assignment L with |L(v)|≥ m for all v∈ V(G). In this note, it is proved that every toroidal graph, which contains no adjacent triangles and contains no 6-cycles and l-cycles for some l ∈ \5,7\, is (3,1)^*-choosable.