complete bipartite graph

List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★

Author(s): Allagan

Question Given $a,b\geq2$ , what is the smallest integer $t\geq0$ such that $\chi_\ell(K_{a,b}+K_t)= \chi(K_{a,b}+K_t)$ ?

Posted by Jon Noel
updated April 12th, 2014

Conjecture If $G$ is a simple graph which can be written as an union of $m$ edge-disjoint complete bipartite graphs, then $\chi(G) \le m+1$ .

Posted by mdevos
updated February 26th, 2010

Author(s): Turan

The crossing number $cr(G)$ of $G$ is the minimum number of crossings in all drawings of $G$ in the plane.

Conjecture $\displaystyle cr(K_{m,n}) = \floor{\frac m2} \floor{\frac {m-1}2} \floor{\frac n2} \floor{\frac {n-1}2}$

Posted by Robert Samal
updated May 11th, 2007