We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an exp...
Testing a property P of graphs in the bounded degree model is the following computational problem: given a graph G of bounded degree d we should distinguish (with probability 0.9,...
A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fáry’s Theorem is established. A purely combinatorial de...
Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R(G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric differenc...
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number k of pieces such that contracting any piece results in a graph of bou...
Erik D. Demaine, MohammadTaghi Hajiaghayi, Bojan M...