Mycielskian graph M15
Name mycielskian15
Group Mycielski
Matrix ID 2771
Num Rows 24,575
Num Cols 24,575
Nonzeros 11,111,110
Pattern Entries 11,111,110
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 M15.                                                  
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 (M15) include the following:             
 * M15 has a minimum chromatic number of 15.                            
 * M15 is triangle-free (i.e. no cycles of length 3 exist).             
 * M15 has a Hamiltonian cycle.                                         
 * M15 has a clique number of 2.                                        
 * M15 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.