... and suppose that M is a matching that is larger than M. Define a subgraph H of G as follows: Let V(H) = V(G) and let E(H) be the set of edges of G ... Before we see Hall's classic matching theorem, we need to define one more term.
This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA.
[269] W. T. Tutte, Thefactorization oflinear graphs, J. London Math. Soc. 22 (1947), no. 2, 107–111. ... [279] H. Walther and H. J. Voss, ̈Uber Kreise in Graphen, VEB Deutscher Verlag der Wissenschaften, Berlin, 1974.
... (pigeonholes) and k + 1 = 4, or, k = 3. Among any kn + 1 = 10 balls (pigeons), four of them are of same colour. (ii) The minimum number of faculties in an institute to be sure that four of them are born in the same month can be ensured ...
This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA.