In graph theory, an overfull graph is a graph whose size is greater than the product of its maximum degree and half of its order floored, i.e. | E | > Δ ( G ) ⌊ | V | / 2 ⌋ {\displaystyle |E|>\Delta (G)\lfloor |V|/2\rfloor } where | E | {\displaystyle |E|} is the size of G, Δ ( G ) {\displaystyle \displaystyle \Delta (G)} is the maximum degree of G, and | V | {\displaystyle |V|} is the order of G. The concept of an overfull subgraph, an overfull graph that is a subgraph, immediately follows. An alternate, stricter definition of an overfull subgraph S of a graph G requires Δ ( G ) = Δ ( S ) {\displaystyle \displaystyle \Delta (G)=\Delta (S)} .