We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...
As graph models are applied to more widely varying fields, researchers struggle with tools for exploring and analyzing these structures. We describe GUESS, a novel system for grap...
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclid...
Although graphs are very common in computer science, they are still very difficult to handle for proof assistants as proving properties of graphs may require heavy computations. T...
Let H be a graph, and let CH(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating CH(G). Previous res...