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12 papers · 2 filters
Unexpected behaviour of crossing sequences
Matt DeVos, Bojan Mohar, Robert Samal
The n-th crossing number of a graph G, denoted cr_n(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a>b>0, the…
The excluded minor structure theorem with planarly embedded wall
Bojan Mohar
A graph is nearly embedded in a surface if it consists of graph that is embedded in the surface, together with a bounded number of vortices having no large transactions. It i…
Strong embeddings of minimum genus
Bojan Mohar
A "folklore conjecture, probably due to Tutte" (as described in [P.D. Seymour, Sums of circuits, Graph theory and related topics (Proc. Conf., Univ. Waterloo, 1977), pp. 341-355, A…
Crossing-critical graphs with large maximum degree
Zdenek Dvorak, Bojan Mohar
A conjecture of Richter and Salazar about graphs that are critical for a fixed crossing number is that they have bounded bandwidth. A weaker well-known conjecture of Richter is…
Spectral radius of finite and infinite planar graphs and of graphs of bounded genus
Zdenek Dvorak, Bojan Mohar
It is well known that the spectral radius of a tree whose maximum degree is cannot exceed . In this paper we derive similar bounds for arbitrary planar graphs and…
Domination number of cubic graphs with large girth
Daniel Kral, Petr Skoda, Jan Volec
We show that every n-vertex cubic graph with girth at least g have domination number at most 0.299871n+O(n/g)<3n/10+O(n/g).