5 papers · 1 filter
Strengthened chain theorems for different versions of 4-connectivity
Guoli Ding, Chengfu Qin
The chain theorem of Tutte states that every 3-connected graph can be constructed from a wheel by repeatedly adding edges and splitting vertices. It is not difficult to prove…
On Gupta's Co-density Conjecture
Yan Cao, Guantao Chen, Guoli Ding +2
Let be a multigraph. The {\em cover index} of is the greatest integer for which there is a coloring of with colors such that each vertex of is…
Graphs without large -minors
Guoli Ding
The purpose of this paper is to characterize graphs that do not have a large -minor. As corollaries, it is proved that, for any given positive integer , every sufficien…
On almost-planar graphs
Guoli Ding, Joshua Fallon, Emily Marshall
A nonplanar graph G is called almost-planar if for every edge e of G, at least one of G\e and G/e is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his d…
Unavoidable Parallel Minors of 4-Connected Graphs
Carolyn Chun, Guoli Ding, Bogdan Oporowski +1
A parallel minor is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer k, every internally 4-connected…