Mycielskian graph M16
Name mycielskian16
Group Mycielski
Matrix ID 2772
Num Rows 49,151
Num Cols 49,151
Nonzeros 33,382,480
Pattern Entries 33,382,480
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 M16.                                                  
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 (M16) include the following:             
 * M16 has a minimum chromatic number of 16.                            
 * M16 is triangle-free (i.e. no cycles of length 3 exist).             
 * M16 has a Hamiltonian cycle.                                         
 * M16 has a clique number of 2.                                        
 * M16 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.