  A vertex of a graph is bisimplicial if the set of its neighbors is the union
of two cliques; a graph is quasi-line if every vertex is bisimplicial. A recent
result of Chudnovsky and Seymour asserts that every non-empty even-hole-free
graph has a bisimplicial vertex. Both Hadwiger's conjecture and the
Erd\H{o}s-Lov\'asz Tihany conjecture have been shown to be true for quasi-line
graphs, but are open for even-hole-free graphs. In this note, we prove that for
all $k\ge7$, every even-hole-free graph with no $K_k$ minor is
$(2k-5)$-colorable; every even-hole-free graph $G$ with
$\omega(G)<\chi(G)=s+t-1$ satisfies the Erd\H{o}s-Lov\'asz Tihany conjecture
provided that $ t\ge s> \chi(G)/3$. Furthermore, we prove that every
$9$-chromatic graph $G$ with $\omega(G)\le 8$ has a $K_4\cup K_6$ minor. Our
proofs rely heavily on the structural result of Chudnovsky and Seymour on
even-hole-free graphs.
