G is a well-covered graph provided all its maximal stable sets are of the same size (Plummer, 1970). S is a local maximum stable set of G, and we denote by S (G), if S is a maxim...
Providing a complete description of the stable set polytopes of claw-free graphs is a longstanding open problem since almost twenty years. Eisenbrandt et al. recently achieved a b...
To decide whether a line graph (hence a claw-free graph) of maximum degree five admits a stable cutset has been proven to be an NP-complete problem. The same result has been known...
We introduce some equivalence relations on graphs and posets and prove that they are closed under the cartesian product operation. These relations concern the edge-isoperimetric p...
Let G be a simple graph and f : V (G) → {1, 3, 5, ...} an odd integer valued function defined on V (G). A spanning subgraph F of G is called a (1, f)odd factor if dF (v) ∈ {1...