The properties of connected matchings Hadwiger's well known conjecture, which states that any graph G has a K χ(G) minor, where χ(G) is the chromatic number of G, are described. In Hadwiger's conjecture, α(G) denotes the independence number of G, namely the maximum number of pairwise nonadjacent vertices in G. One of the Hadwiger's conjecture states that there exists some constant c such that every graph G with ct vertices and with α(G) = 2 contains a connected matching of size t. The other conjecture states that every graph G with 4t-1 vertices and with α(G) = 2 contains a connected matching of size t.
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics