Minimum total coloring of planar graphs with maximum degree 8

Liting Wang, Huijuan Wang () and Weili Wu
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Liting Wang: Qingdao University
Huijuan Wang: Qingdao University
Weili Wu: University of Texas at Dallas

Journal of Combinatorial Optimization, 2023, vol. 45, issue 2, No 28, 11 pages

Abstract: Abstract We define G to be a planar graph with maximum degree $$\varDelta $$ Δ . Suppose $$\varDelta \ge 8$$ Δ ≥ 8 and G has no adjacent p,q-cycles for some p, $$q\in \{3,4,5,6,7,8\}$$ q ∈ { 3 , 4 , 5 , 6 , 7 , 8 } , then G can be totally colored by $$(\varDelta +1)$$ ( Δ + 1 ) colors.

Keywords: Minimum total coloring; Planar graph; Maximum degree (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01011-y

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