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10 papers · 2 filters
Extremal results regarding -minors in graphs of girth at least 5
Elad Aigner-Horev, Roi Krakovski
We prove that every 6-connected graph of girth has a -minor and thus settle the Jorgensen conjecture for graphs of girth . Relaxing the assumption on the gir…
Average Degree in Graph Powers
Matt DeVos, Jessica McDonald, Diego Scheide
The kth power of a simple graph G, denoted G^k, is the graph with vertex set V(G) where two vertices are adjacent if they are within distance k in G. We are interested in finding l…
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]…