We conjecture that every planar graph of odd-girth 2k + 1 admits a homomorphism to Cayley graph C(Z2k+1 2 , S2k+1), with S2k+1 being the set of (2k + 1)vectors with exactly two co...
: We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3 8 n. This was suggested and later conjectured b...
We study the topological simplification of graphs via random embeddings, leading ultimately to a reduction of the Gupta-Newman-Rabinovich-Sinclair (GNRS) L1 embedding conjecture t...
We prove that, for every two n-node non-star trees of diameter at most four, there exists an n-node planar graph containing them as edge-disjoint subgraphs.
We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization...