Mycielskian graph M10
Name mycielskian10
Group Mycielski
Matrix ID 2766
Num Rows 767
Num Cols 767
Nonzeros 44,392
Pattern Entries 44,392
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 M10.                                                  
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 (M10) include the following:             
 * M10 has a minimum chromatic number of 10.                            
 * M10 is triangle-free (i.e. no cycles of length 3 exist).             
 * M10 has a Hamiltonian cycle.                                         
 * M10 has a clique number of 2.                                        
 * M10 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.