Mycielskian graph M18
Name mycielskian18
Group Mycielski
Matrix ID 2774
Num Rows 196,607
Num Cols 196,607
Nonzeros 300,933,832
Pattern Entries 300,933,832
Kind Undirected Graph
Symmetric Yes
Date 2018
Author J. Mycielski
Editor S. Kolodziej
Structural Rank
Structural Rank Full
Num Dmperm Blocks
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate no
Positive Definite no
Type binary
Download MATLAB Rutherford Boeing Matrix Market
Mycielskian graph M18.                                                  
The Mycielskian graph sequence generates graphs that are triangle-free  
and with a known chromatic number (i.e. the minimum number of colors    
required to color the vertices of the graph).                           
Known properties of this graph (M18) include the following:             
 * M18 has a minimum chromatic number of 18.                            
 * M18 is triangle-free (i.e. no cycles of length 3 exist).             
 * M18 has a Hamiltonian cycle.                                         
 * M18 has a clique number of 2.                                        
 * M18 is factor-critical, meaning every subgraph of |V|-1 vertices has 
   a perfect matching.                                                  
Mycielski graphs were first described by Jan Mycielski in the following 
    Mycielski, J., 1955. Sur le coloriage des graphes. Colloq. Math.,   
    3: 161-162.