Name
Abstract | ||
|---|---|---|
A total coloring is equitable if the number of elements colored by any two distinct colors differs by at most one. The equitable total chromatic number of a graph (χe″) is the smallest integer for which the graph has an equitable total coloring. Wang (2002) conjectured that Δ+1≤χe″≤Δ+2. In 1994, Fu proved that there exist equitable (Δ + 2)-total colorings for all complete r-partite p-balanced graphs of odd order. For the even case, he determined that χe″≤Δ+3. Silva, Dantas and Sasaki (2018) verified Wang's conjecture when G is a complete r-partite p-balanced graph, showing that χe″=Δ+1 if G has odd order, and χe″≤Δ+2 if G has even order. In this work we improve this bound by showing that χe″=Δ+1 when G is a complete r-partite p-balanced graph with r ≥ 4 even and p even, and for r odd and p even. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.entcs.2019.08.060 | Electronic Notes in Theoretical Computer Science |
Keywords | DocType | Volume |
Equitable total coloring,complete r-partite p-balanced graphs,graph coloring | Journal | 346 |
ISSN | Citations | PageRank |
1571-0661 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anderson G. da Silva | 1 | 0 | 0.34 |
| Simone Dantas | 2 | 119 | 24.99 |
| D. Sasaki | 3 | 7 | 3.94 |