Mycielskian graph M11
Name mycielskian11
Group Mycielski
Matrix ID 2767
Num Rows 1,535
Num Cols 1,535
Nonzeros 134,710
Pattern Entries 134,710
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 M11.                                                  
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 (M11) include the following:             
 * M11 has a minimum chromatic number of 11.                            
 * M11 is triangle-free (i.e. no cycles of length 3 exist).             
 * M11 has a Hamiltonian cycle.                                         
 * M11 has a clique number of 2.                                        
 * M11 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.