31 citations · 298 across the 114 of their papers we have counts for
9 papers · 1 filter
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…
Chromatic number and complete graph substructures for degree sequences
Zdenek Dvorak, Bojan Mohar
Given a graphic degree sequence , let (respectively , , and ) denote the maximum value of the chromatic number (respectively, the size of the largest cl…
An Eberhard-like theorem for pentagons and heptagons
Matt DeVos, Agelos Georgakopoulos, Bojan Mohar +1
Eberhard proved that for every sequence of non-negative integers satisfying Euler's formula , there are infinitely many…
Simplices and spectra of graphs, continued
Bojan Mohar, Igor Rivin
In this note we show that the n-2-dimensional volumes of codimension 2 faces of an n-dimensional simplex are algebraically independent quantities of the volumes of its edge-lengths…
A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm
Bojan Mohar, Jesus Salas
We prove that for the class of three-colorable triangulations of a closed oriented surface, the degree of a four-coloring modulo 12 is an invariant under Kempe changes. We use this…