%0 Generic %1 henderson2020bounds %A Henderson, M. %A Hilton, A. J. W. %A Jothi, R. Mary Jeya %D 2020 %K edge_colouring list_colouring %T Bounds Related to The Edge-List Chromatic and Total Chromatic Numbers of a Simple Graph %U http://arxiv.org/abs/2004.01848 %X We show that for a simple graph $G$, $c'(G)łeq\Delta(G)+2$ where $c'(G)$ is the choice index (or edge-list chromatic number) of $G$, and $\Delta(G)$ is the maximum degree of $G$. As a simple corollary of this result, we show that the total chromatic number $\chi_T(G)$ of a simple graph satisfies the inequality $\chi_T(G)łeq\ \Delta(G)+4$ and the total choice number $c_T(G)$ also satisfies this inequality. We also relate these bounds to the Hall index and the Hall condition index of a simple graph, and to the total Hall number and the total Hall condition number of a simple graph.

@misc{henderson2020bounds, abstract = {We show that for a simple graph $G$, $c'(G)\leq\Delta(G)+2$ where $c'(G)$ is the choice index (or edge-list chromatic number) of $G$, and $\Delta(G)$ is the maximum degree of $G$. As a simple corollary of this result, we show that the total chromatic number $\chi_T(G)$ of a simple graph satisfies the inequality $\chi_T(G)\leq\ \Delta(G)+4$ and the total choice number $c_T(G)$ also satisfies this inequality. We also relate these bounds to the Hall index and the Hall condition index of a simple graph, and to the total Hall number and the total Hall condition number of a simple graph.}, added-at = {2020-05-20T14:12:00.000+0200}, author = {Henderson, M. and Hilton, A. J. W. and Jothi, R. Mary Jeya}, biburl = {https://www.bibsonomy.org/bibtex/25bb39ef12def44e0cba97afc77a88db6/j.c.m.janssen}, description = {Bounds Related to The Edge-List Chromatic and Total Chromatic Numbers of a Simple Graph}, interhash = {a241122ce97b537ea5e6ec85caaca7ca}, intrahash = {5bb39ef12def44e0cba97afc77a88db6}, keywords = {edge_colouring list_colouring}, note = {cite arxiv:2004.01848}, timestamp = {2020-05-20T14:12:00.000+0200}, title = {Bounds Related to The Edge-List Chromatic and Total Chromatic Numbers of a Simple Graph}, url = {http://arxiv.org/abs/2004.01848}, year = 2020 }