![]() ![]() Qi, M.K., Zhang, X.: Odd coloring of two subclasses of planar graphs (2022). Petruševski, M., Škrekovski, R.: Coloring with neighborhood parity condition (2022). Petr, J., Portier, J.: The odd chromatic number of a planar graph is at most 8 (2022). For every two positive integers a and b such that. In fact, much more can be said: Let n be a positive integer. And, there is no possible improvement of any of these bounds. Metrebian, H.: Odd coloring on the torus (2022). This is the Nordhaus-Gaddum Theorem: If G is a graph of order n, then. arXiv: 2202.02586v4Įven, G., Lotker, Z., Ron, D., Smorodinsky, S.: Conflict-free colorings of simple geometric regions with applications to frequency assignment in cellular networks. You dont need to prove that your graph is triangle. 02.73 ORD (8 points) DMmini 6.1.59 (triangle-free graph of chromatic number 4 with 11 vertices). 02.71 DO Find a graph with 6 vertices such that chi(G)4 but omega(G)3. arXiv:2201.01455v1Ĭranston, D.W., Lafferty, M., Song, Z.-X.: A note on odd coloring of 1-planar graphs (2022). On the other hand, there is an important class of graphs where the chromatic number and the clique number are equal. ![]() arXiv: 2202.11267v1Ĭranston, D.W.: Odd Colorings of Sparse Graphs (2022). Request PDF Reexploring the upper bound for the chromatic number of graphs The upper bound of the chromatic number of simple graphs is explored. arXiv: 2201.03608v1Ĭho, E.-K., Choi, I., Kwon, H., Park, B.: Odd coloring of sparse graphs and planar graphs. proved that every graph with no odd minor is -colorable. This is a strengthening of the famous Hadwiger's Conjecture. GTM 244, Springer, New York (2008)Ĭaro, Y., Petruševski, M., Škrekovski, R.: Remarks on odd colorings of graphs. A new upper bound on the chromatic number of graphs with no odd minor Sergey Norin, Zi-Xia Song Gerards and Seymour conjectured that every graph with no odd minor is -colorable. Bondy, J.A., Murty, U.S.R.: Graph Theory. In this paper, we further study the relationship between the D P -chromatic number of a graph G and its variation of Randi index, and the following upper bound for D P ( G) in terms of its variation of Randi index is deduced. ![]()
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