We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, ...
Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an ...
Mihyun Kang, Oleg Pikhurko, Alexander Ravsky, Math...
An induced matching in graph G is a matching which is an induced subgraph of G. Clearly, among two vertices with the same neighborhood (called twins) at most one is matched in any...
Rok Erman, Lukasz Kowalik, Matjaz Krnc, Tomasz Wal...
We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detail...
Hajo Broersma, Fedor V. Fomin, Jan Kratochví...
Graph sub-isomorphism is a very common approach to solving pattern search problems, but this is a NP-complete problem. This way, it is necessary to invest in research of approxima...