Mycielskian graph M6
Name mycielskian6
Group Mycielski
Matrix ID 2762
Num Rows 47
Num Cols 47
Nonzeros 472
Pattern Entries 472
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 M6.                                                   
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 (M6) include the following:              
 * M6 has a minimum chromatic number of 6.                              
 * M6 is triangle-free (i.e. no cycles of length 3 exist).              
 * M6 has a Hamiltonian cycle.                                          
 * M6 has a clique number of 2.                                         
 * M6 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.