An Improvement of Hind's Upper Bound on the Total Chromatic Number
نویسندگان
چکیده
The purpose of this note is to improve Hind's theorem for graphs with large chromatic number by essentially reducing the power of / from | to | + e (the exact statement of our result is given in equations (4)-(6) below). Our proof uses a lemma which in words states that, if we assign to each vertex x in a fc-chromatic r-edge-chromatic multigraph a colour/(x) from {1,2,. . . ,r}, then there exists a proper (r + fc)-edge-colouring which on each edge xy assigns a colour from {1,2,... , r + k} — f(x) — f(y). Using terminology from our earlier work [2], we can formulate this as
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 5 شماره
صفحات -
تاریخ انتشار 1996