29 citations · 62 across the 8 of their papers we have counts for
14 papers
Reflexive coloring complexes for 3-edge-colorings of cubic graphs
Fiachra Knox, Bojan Mohar, Nathan Singer
Given a 3-colorable graph , the 3-coloring complex is the graph whose vertices are all the independent sets which occur as color classes in some 3-coloring of . Two co…
Cops and Robbers on graphs of bounded diameter
Seyyed Aliasghar Hosseini, Fiachra Knox, Bojan Mohar
The game of Cops and Robbers is a well known game played on graphs. In this paper we consider the class of graphs of bounded diameter. We improve the strategy of cops and previousl…
Fractional decompositions and the smallest-eigenvalue separation
Fiachra Knox, Bojan Mohar
A new method is introduced for bounding the separation between the value of and the smallest eigenvalue of a non-bipartite -regular graph. The method is based on fractional…
Cops and robbers on oriented toroidal grids
Sebastian Gonzalez Hermosillo de la Maza, Seyyed Aliasghar Hosseini, Fiachra Knox +2
The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Kle…
A golden ratio inequality for vertex degrees of graphs
Fiachra Knox, Bojan Mohar, David R. Wood
Motivated by the study of the crossing number of graphs, it is shown that, for trees, the sum of the products of the degrees of the end-vertices of all edges has an upper bound in…
Maximum number of colourings. II. 5-chromatic graphs
Fiachra Knox, Bojan Mohar
In 1971, Tomescu conjectured [Le nombre des graphes connexes -chromatiques minimaux aux sommets étiquetés, C. R. Acad. Sci. Paris 273 (1971), 1124--1126] that every connected gr…