Description of mycielski

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mycielski

PURPOSE

mycielski(g,n) --- create n'th order Mycielski graph (n > 0)

SYNOPSIS

function mycielski(g,h)

DESCRIPTION

 mycielski(g,n) --- create n'th order Mycielski graph (n > 0)
 mycielski(g,h) --- apply Mycielski step to h to give g
 e.g., mycielski(g,3) overwrites G with the Grotztsch graph
 Thanks: Kim Tucker

CROSS-REFERENCE INFORMATION

This function calls:

• complete complete: build complete and complete multipartite graphs
• fast_set_matrix fast_set_matrix(g,A) --- overwrite the adjacency matrix of g with A
• matrix matrix(g) --- return (a copy of) the adjacency matrix of g
• mycielski mycielski(g,n) --- create n'th order Mycielski graph (n > 0)
• rmxy rmxy(g) --- erase g's embedding

This function is called by:

• mycielski mycielski(g,n) --- create n'th order Mycielski graph (n > 0)

SOURCE CODE

0001 function mycielski(g,h)
0002 % mycielski(g,n) --- create n'th order Mycielski graph (n > 0)
0003 % mycielski(g,h) --- apply Mycielski step to h to give g
0004 % e.g., mycielski(g,3) overwrites G with the Grotztsch graph
0005 % Thanks: Kim Tucker
0006 
0007 
0008 % if 2nd argument is a graph, apply construction one time
0009 
0010 if (isa(h,'graph'))
0011     B = matrix(h);
0012     n = length(B);
0013 
0014     A = [ B, B,  zeros(n,1);
0015           B,   zeros(n),  ones(n,1);
0016           zeros(1,n), ones(1,n), 0 ];
0017     fast_set_matrix(g,A);
0018     rmxy(g);
0019     return
0020 end
0021 
0022 
0023 % otherwise, 2nd argument is an integer
0024 
0025 h = floor(h);
0026 
0027 if (h<=0)
0028     complete(g,1);
0029     return
0030 end
0031 
0032 if (h == 1)
0033     complete(g,2);
0034     return
0035 end
0036 
0037 mycielski(g,h-1);
0038 mycielski(g,g);

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