47 citations · 178 across the 44 of their papers we have counts for
7 papers · 1 filter
Longest Paths in Circular Arc Graphs
Felix Joos
As observed by Rautenbach and Sereni (arXiv:1302.5503) there is a gap in the proof of the theorem of Balister et al. (Longest paths in circular arc graphs, Combin. Probab. Comput.,…
Forests and Trees among Gallai Graphs
Felix Joos, Van Bang Le, Dieter Rautenbach
The Gallai graph of a graph has the edges of as its vertices and two distinct vertices and of are adjacent in if the edges and of a…
Induced Matchings in Subcubic Graphs
Felix Joos, Dieter Rautenbach, Thomas Sasse
We prove that a cubic graph with edges has an induced matching with at least edges. Our result generalizes a result for planar graphs due to Kang, Mnich, and Müller (Indu…
The Cycle Spectrum of Claw-free Hamiltonian Graphs
Jonas Eckert, Felix Joos, Dieter Rautenbach
If is a claw-free hamiltonian graph of order and maximum degree with , then has cycles of at least $\min\left\{ n,\left\lceil\frac{3}{2}Δ\right\rceil\righ…
Random Subgraphs in Sparse Graphs
Felix Joos
We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solve the problem for Cartesian powers of arbitrar…
Independence and Matching Number in Graphs with Maximum Degree 4
Felix Joos
We prove that and for every triangle-free graph with maximum degree at most , where is the independenc…
A Characterization of Mixed Unit Interval Graphs
Felix Joos
We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper supercla…