Mycielskian graph M19
Name mycielskian19
Group Mycielski
Matrix ID 2775
Num Rows 393,215
Num Cols 393,215
Nonzeros 903,194,710
Pattern Entries 903,194,710
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 M19.                                                  
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 (M19) include the following:             
 * M19 has a minimum chromatic number of 19.                            
 * M19 is triangle-free (i.e. no cycles of length 3 exist).             
 * M19 has a Hamiltonian cycle.                                         
 * M19 has a clique number of 2.                                        
 * M19 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.