Mycielskian graph M14
Name mycielskian14
Group Mycielski
Matrix ID 2770
Num Rows 12,287
Num Cols 12,287
Nonzeros 3,695,512
Pattern Entries 3,695,512
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 M14.                                                  
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 (M14) include the following:             
 * M14 has a minimum chromatic number of 14.                            
 * M14 is triangle-free (i.e. no cycles of length 3 exist).             
 * M14 has a Hamiltonian cycle.                                         
 * M14 has a clique number of 2.                                        
 * M14 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.