Mycielskian graph M9
Name mycielskian9
Group Mycielski
Matrix ID 2765
Num Rows 383
Num Cols 383
Nonzeros 14,542
Pattern Entries 14,542
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 M9.                                                   
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 (M9) include the following:              
 * M9 has a minimum chromatic number of 9.                              
 * M9 is triangle-free (i.e. no cycles of length 3 exist).              
 * M9 has a Hamiltonian cycle.                                          
 * M9 has a clique number of 2.                                         
 * M9 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.