Validity of the weakened Hadwiger hypothesis
Venn diagrams and symmetric chain decompositions in the Boolean lattice.
Venn diagrams with few vertices.
Vertex coloring the square of outerplanar graphs of low degree
Vertex colorings of the square of an outerplanar graph have received a lot of attention recently. In this article we prove that the chromatic number of the square of an outerplanar graph of maximum degree Δ = 6 is 7. The optimal upper bound for the chromatic number of the square of an outerplanar graph of maximum degree Δ ≠ 6 is known. Hence, this mentioned chromatic number of 7 is the last and only unknown upper bound of the chromatic number in terms of Δ.