Mycielskian graph M12
Name mycielskian12
Group Mycielski
Matrix ID 2768
Num Rows 3,071
Num Cols 3,071
Nonzeros 407,200
Pattern Entries 407,200
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 M12.                                                  
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 (M12) include the following:             
 * M12 has a minimum chromatic number of 12.                            
 * M12 is triangle-free (i.e. no cycles of length 3 exist).             
 * M12 has a Hamiltonian cycle.                                         
 * M12 has a clique number of 2.                                        
 * M12 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.