Felix Joos

Induced Matchings in Subcubic Graphs

We prove that a cubic graph with

Long cycles through prescribed vertices have the Erdős‐Pósa property

m

How to Determine if a Random Graph with a Fixed Degree Sequence Has a Giant Component

edges has an induced matching with at least

Induced Matchings in Graphs of Bounded Maximum Degree

m/9

Maximum induced matchings close to maximum matchings

edges. Our result generalizes a result for planar graphs due to Kang, Mnich, and Muller (SIAM J. Discrete Math., 26 (2012), pp. 1383--1411) and solves a conjecture of Henning and Rautenbach.

A Note on Longest Paths in Circular Arc Graphs

We prove that for every graph, any vertex subset S, and given integers k, `: there are k disjoint cycles of length at least ` that each contain at least one vertex from S, or a vertex set of size O(` · k log k) that meets all such cycles. This generalises previous results of Fiorini and Hendrickx and of Pontecorvi and Wollan. In addition, we describe an algorithm for our main result that runs in O(k log k · s · (f(`) · n+m)) time, where s denotes the cardinality of S.

Structural Parameterizations for Boxicity

For a fixed degree sequence

A Stronger Bound for the Strong Chromatic Index

{\mathcal {D}}=(d_1,\ldots ,d_n)