永並 健吾

A graph G is (s(1), s(2), ... , s(k))-linked, if for any k disjoint vertex sets S-1, S-2, ... , S-k with vertical bar S-i vertical bar <= s(i), G has k vertex-disjoint connected subgraphs G(1), G(2), ... , G(k) such that S-i subset of V(G(i)) for ...

We consider a proper coloring of a plane graph such that no face is rainbow, where a face is rainbow if any two vertices on its boundary have distinct colors. Such a coloring is said to be proper anti-rainbow. A plane quadrangulation G is a plane ...