an:01062589
Zbl 0883.05053
Borodin, O. V.; Kostochka, A. V.; Woodall, D. R.
Total colorings of planar graphs with large maximum degree
EN
J. Graph Theory 26, No. 1, 53-59 (1997).
00042694
1997
j
05C15 05C10 05C35
planar graph; maximum degree; total chromatic number
The authors prove that for any planar graph \(G\) with maximum degree \(\Delta\geq 11\), its total chromatic number \(\chi_T(G)= \Delta+1\). This result improves an earlier result due to the same authors. The proof begins by finding some ``reducible configurations'' of a minimum counterexample \(G=(V,E)\) (a counterexample with \(|V|+|E|\) minimum) and then using ``discharging'' to obtain a contradiction.
H.P.Yap (Singapore)