We prove that with high probability a skip graph contains a 4-regular expander as a subgraph, and estimate the quality of the expansion via simulations. As a consequence skip grap...
Abstract. The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppste...
One of the basic results in graph theory is Dirac's theorem, that every graph of order n 3 and minimum degree n/2 is Hamiltonian. This may be restated as: if a graph of ord...
Multicut is a fundamental network communication and connectivity problem. It is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimu...
For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In (J Graph Theory 11:399–407 (1987)), Broersma and Veldman propo...