31 citations · 298 across the 114 of their papers we have counts for
8 papers · 2 filters
A Linear Lower Bound for the Square Energy of Graphs
Saieed Akbari, Hitesh Kumar, Bojan Mohar +1
Let be a graph of order with eigenvalues . Let \[s^+(G)=\sum_{λ_i>0} λ_i^2, \qquad s^-(G)=\sum_{λ_i<0} λ_i^2.\] The smaller value, $s(G)=\min\{s^+(…
Bipartite graphs are -choosable
Peter Bradshaw, Bojan Mohar, Ladislav Stacho
Alon and Krivelevich conjectured that if is a bipartite graph of maximum degree , then the choosability (or list chromatic number) of satisfies $χ_{\ell}(G) = O \left (…
Clustered Colouring of Graph Products
Rutger Campbell, J. Pascal Gollin, Kevin Hendrey +5
A colouring of a graph has clustering if the maximum number of vertices in a monochromatic component equals . Motivated by recent results showing that many natural graph…
Guarding isometric subgraphs and Cops and Robber in planar graphs
Sebastián González Hermosillo de la Maza, Bojan Mohar
In the game of Cops and Robbers, one of the most useful results is that an isometric path in a graph can be guarded by one cop. In this paper, we introduce the concept of wide shad…
Three-edge-coloring projective planar cubic graphs: A generalization of the Four Color Theorem
Yuta Inoue, Ken-ichi Kawarabayashi, Atsuyuki Miyashita +2
We prove that every cyclically 4-edge-connected cubic graph that can be embedded in the projective plane, with the single exception of the Petersen graph, is 3-edge-colorable. In o…
Sharing tea on a graph
J. Pascal Gollin, Kevin Hendrey, Hao Huang +6
Motivated by the analysis of consensus formation in the Deffuant model for social interaction, we consider the following procedure on a graph . Initially, there is one unit of t…
Strong log-convexity of genus sequences
Bojan Mohar
For a graph , and a nonnegative integer , let be the number of -cell embeddings of in an orientable surface of genus (counted up to the combinatorial home…
Cops and Robber on Hyperbolic Manifolds
Vesna Iršič, Bojan Mohar, Alexandra Wesolek
The Cops and Robber game on geodesic spaces is a pursuit-evasion game with discrete steps which captures the behavior of the game played on graphs, as well as that of continuous pu…