31 citations · 298 across the 114 of their papers we have counts for
8 papers · 2 filters
Expected Crossing Numbers
Bojan Mohar, Tamon Stephen
The expected value for the weighted crossing number of a randomly weighted graph is studied. A variation of the Crossing Lemma for expectations is proved. We focus on the case wher…
Packing triangles in weighted graphs
Guillaume Chapuy, Matt DeVos, Jessica McDonald +2
Tuza conjectured that for every graph , the maximum size of a set of edge-disjoint triangles and minimum size of a set of edges meeting all triangles satisfy .…
Star chromatic index
Zdeněk Dvořák, Bojan Mohar, Robert Šámal
The star chromatic index of a graph is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colo…
Spectrally degenerate graphs: Hereditary case
Zdenek Dvorak, Bojan Mohar
It is well known that the spectral radius of a tree whose maximum degree is D cannot exceed 2sqrt{D-1}. Similar upper bound holds for arbitrary planar graphs, whose spectral radius…
Local chromatic number of quadrangulations of surfaces
Bojan Mohar, Gábor Simonyi, Gábor Tardos
The local chromatic number of a graph was introduced by Erdős et al. [4]. In [17] a connection to topological properties of (a box complex of) the graph was established and in [18]…
Kempe equivalence of edge-colourings in subcubic and subquartic graphs
Jessica McDonald, Bojan Mohar, Diego Scheide
It is proved that all 4-edge-colourings of a (sub)cubic graph are Kempe equivalent. This resolves a conjecture of the second author. In fact, it is found that the maximum degree De…
A strengthening and a multipartite generalization of the Alon-Boppana-Serre Theorem
Bojan Mohar
The Alon-Boppana theorem confirms that for every and every integer , there are only finitely many -regular graphs whose second largest eigenvalue is at most $2\sqrt…
Asymptotic enumeration and limit laws for graphs of fixed genus
Guillaume Chapuy, Eric Fusy, Omer Gimenez +2
It is shown that the number of labelled graphs with n vertices that can be embedded in the orientable surface S_g of genus g grows asymptotically like …