Fiachra Knox

activity

20102020

most citedPolynomial-time perfect matchings in dense hypergraphs

29 citations · 62 across the 8 of their papers we have counts for

collaborators

Showing 2017Show all

3 papers · 1 filter

math.CO2017★ 3 cited

Maximum number of colourings. II. 5-chromatic graphs

Fiachra Knox, Bojan Mohar

In 1971, Tomescu conjectured [Le nombre des graphes connexes $k$ -chromatiques minimaux aux sommets étiquetés, C. R. Acad. Sci. Paris 273 (1971), 1124--1126] that every connected gr…

math.CO2017

Maximum number of colourings. I. 4-chromatic graphs

Fiachra Knox, Bojan Mohar

It is proved that every connected graph $G$ on $n$ vertices with $χ (G) \geq 4$ has at most $k (k - 1)^{n - 3} (k - 2) (k - 3)$ $k$ -colourings for every $k \geq 4$ . Equality holds for some (an…

math.CO2017

Linear Bound for Majority Colourings of Digraphs

Fiachra Knox, Robert Šámal

Given $η \in [0, 1]$ , a colouring $C$ of $V (G)$ is an $η$ -majority colouring if at most $η d^{+} (v)$ out-neighbours of $v$ have colour $C (v)$ , for any $v \in V (G)$ . We show that every…