Reconfiguration on sparse graphs

Reconfiguration on Sparse Graphs

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions Ss and St of size k, whether it is possible to transform Ss into St by a sequence of vertex additions and deletions such that each intermediate set is also a feasible solution of size bounded by k....

On Graphs Which Contain All Sparse Graphs

On globally sparse Ramsey graphs

We say that a graph G has the Ramsey property w.r.t. some graph F and some integer r ≥ 2, or G is (F, r)-Ramsey for short, if any r-coloring of the edges of G contains a monochromatic copy of F . Rödl and Ruciński asked how globally sparse (F, r)-Ramsey graphs G can possibly be, where the density of G is measured by the subgraph H ⊆ G with the highest average degree. So far, this so-called Rams...

On Coloring of Sparse Graphs

Graph coloring has numerous applications and is a wellknown NP-complete problem. The goal of this paper is to survey recent results of the authors on coloring and improper coloring of sparse graphs and to point out some polynomial-time algorithms for coloring (not necessarily optimal) of graphs with bounded maximum average degree. Mathematics Subject Classification: 05C15, 05C35

A Note on Sparse Random Graphs and Cover Graphs