Month: February 2017

This program is a variation on the solver for 14 vertices. The solver for 15 vertices has the added ingredient that it forces the first seven vertices and the edges that join some of these 7 vertices to each other to form as a subgraph a Moser spindle: a particular 7-vertex, 11-edge graph decribed at… Continue reading Unit distance graph solver for 15 vertices

Starts below, with a fixed number of lines (4 it seems) for each of the 33 edges programmed to be drawn. File name should end in .ps : newpath 73 269 moveto 353 289 lineto stroke newpath 73 269 moveto 353 289 lineto stroke newpath 73 269 moveto 296 440 lineto stroke newpath 73 269… Continue reading PostScript “source code”, 14-vertex 33-edge graph

To know details of a Linux package, example: $ rpm -qi firefox gives this: Name : firefox Relocations: (not relocatable) Version : 45.7.0 Vendor: CentOS Release : 2.el6.centos Build Date: Tue 21 Feb 2017 10:37:31 AM EST Install Date: Wed 22 Feb 2017 02:00:30 PM EST Build Host: c1bm.rdu2.centos.org Group : Applications/Internet Source RPM: firefox-45.7.0-2.el6.centos.src.rpm… Continue reading Useful command: rpm -qi

[david@localhost ~]$ /bin/su – Password: [root@localhost ~]# cd /usr [root@localhost usr]# ls bin etc games include lib lib64 libexec local sbin share src tmp [root@localhost usr]# cd local [root@localhost local]# ls bin etc games include lib lib64 libexec sbin share src [root@localhost local]# cd lib [root@localhost lib]# ls libgmp.a libhistory.so libpari-gmp.so.5 libreadline.so.7 libgmp.la libhistory.so.6 libpari.so… Continue reading My “fix” of reaeadline problem in PARI/gp following #yum update

# yum update broke my patch to using the “right” libreadline library for PARI/gp: [david@localhost ~]$ gp gp: symbol lookup error: /usr/local/lib/libreadline.so.6: undefined symbol: PC $ ls -l /usr/local/lib/ | grep libreadline […] lrwxrwxrwx. 1 root root 16 Feb 23 02:55 libreadline.so -> libreadline.so.6 lrwxrwxrwx. 1 root root 18 Feb 25 02:43 libreadline.so.6 -> libreadline.so.6.3… Continue reading yum update broke my PARI/gp workaround with libreadline

I wrote a modified searcher for 14-vertex, non 3-colorable, unit distance graphs, embeddable in the plane R^2 with edges of length 1 between vertices, at least numerically. The searcher has a randomozing seed constant for the PRNG (pseudo-random number generator): it is the unisgned long long constant: 14502779422240352273ULL present in the array initiaizer code: for(i=0;i<2097152;i++)… Continue reading Unit distance graph searcher for 14 vertices in C

I modified my searcher of unit distance graphs for 13 vertices, so that it works on searching and solving 14-vertex unit distance graphs. I look for 14-vertex unit distance graphs that: (a) are not 3-colorable and (b) have the least possible 4-colorings, up to permutation of the 4 colors, which can be done be 4!… Continue reading “Best candidate” graph, 14 vertices, udg

To open a file for reading in the C programming language, one can pass to fopen a string containing the absolute path to the file. It looks like this: fopen(“/home/david/fname”, “r”) string = “/home/david/fname” = path to file, and “r” for open in read-only mode. Because it’s a statement, it must end with a `;’… Continue reading Simple C test programs that open and read a file

C source code file = /home/david/graphs/golomb18/udgraph13_solverff9789nu97b.c or: udgraph13_solverff9789nu97b.c in directory: /home/david/graphs/golomb18/   23 69 6e 63 6c 75 64 65 20 3c 73 74 64 69 6f 2e 68 3e 0a 23 69 6e 63 6c 75 64 65 20 3c 6d 61 74 68 2e 68 3e 0a 23 64 65 66 69 6e… Continue reading Hexadecimal dump of C source code …

The unit distance graph solver I wrote in the C programming language may have found a unit distance graph with 13 vertices, 30 edges of length one, chromatic number 4, and 212 4-colourings, up to permutation of the 4 colours, where there are 4! = 24 permutations of the colours, say, Red, Green, Blue, and… Continue reading Possible unit distance graph with 13 vertices and 30 edges

After convergence to the unit distance graph equations (vertex to vertex distances are 1 to within 1E-15, according to the 13×13 adjacency matrix adjmat[][] ), the solver checks that no two distinct vertices are “suspiciously close”, which is a good sign they are in fact superposed,what we call a “singular solution”: those are rejected. After… Continue reading new solver 13 vertices: minor source code edit…

udgraph13_solverff9789nu95a.c in /home/david/graphs/golomb18 #include <stdio.h> #include <math.h> #define NUMSTEPS 2500 #define MAXDIFFAT100 ((long double) 18)/((long double) 1) #define MAXDIFFAT50 ((long double) 18)/((long double) 1) #define MAXDIFFAT25 ((long double) 40)/((long double) 1) #define MAXDIFFAT1 ((long double) 40)/((long double) 1) #define MAXDIFFAT200 ((long double) 96)/((long double) 10) #define MAXDIFFAT400 ((long double) 67)/((long double) 1000) #define MAXDIFFAT800 ((long… Continue reading new solver 13 vertices

For the unit distance graphs solver, considering only graphs that can’t be vertex-coloured with 3 colours, but that are 4-colourable, I want to know if there are any repeats in the number of 4-colourings given, which is a complete count, up to permutations of the four colors. For this, I devised the shell script status.sh… Continue reading Useful shell script for latest unit distance graph solver

After 186 minutes running time, the solver has solved at least 15 12-vertex unit distance graphs requiring 4 colours. The first 12-vertex unit distance graph found that was 4-colorable but not 3-colourable had 813 4-colourings, up to permutations of the 4 colours. After 186 minutes, the range in number of 4-colourings for the 12-vertex unit… Continue reading Update on unit distance graph solver output

For 12 vertices, we look for graphs with 21 or more edges. This is because with 12 x-coordinates and 12 y-coordinates, we have 24 variables. A solution to a unit distance graph problem can be translated in the plane, and also rotated. If we fix point A to the origin (0, 0) and require that… Continue reading Update on unit distance graph solver

Notes:  the code for testing for existence of a 3-coloring has been commented out. This was to test for sanity of the rest of the code. The rest of the code passes the sanity test, however gives too much output. udg = “unit distance graph” . It’s debatable whether to test for 3-colorability before or… Continue reading initial draft release of udgraph12_

#include <stdio.h> #include <math.h> #define NUMSTEPS 2000 #define MAXDIFFAT100 ((long double) 30)/((long double) 1) #define MAXDIFFAT50 ((long double) 118)/((long double) 1) #define MAXDIFFAT25 ((long double) 12)/((long double) 1) #define VERBOSE #define VERTEX 12 static unsigned long long Q[2097152],carry=0; unsigned long long B64MWC(void) { unsigned long long t,x; static int j=2097151; j=(j+1)&2097151; x=Q[j]; t=(x<<28)+carry; carry=(x>>36)-(t<x); return… Continue reading initial draft release of udgraph12_solverbb9901a.c

I give the data in the file udgraph_solver301a dot c in hexadecimal representation, byte-by-byte, in the interest of data persistence. The local file udgraph_solver301a dot c contains 11325 bytes of data.   23 69 6e 63 6c 75 64 65 20 3c 73 74 64 69 6f 2e 68 3e 0a 23 69 6e 63… Continue reading udgraph_solver301a dot c, in hexadecimal

#include <stdio.h> #include <math.h> #define NUMSTEPS 510 #define MAXDIFFAT100 ((long double) 110)/((long double) 1000) #define MAXDIFFAT50 ((long double) 14)/((long double) 10) #define MAXDIFFAT25 ((long double) 550)/((long double) 100) static unsigned long long Q[2097152],carry=0; unsigned long long B64MWC(void) { unsigned long long t,x; static int j=2097151; j=(j+1)&2097151; x=Q[j]; t=(x<<28)+carry; carry=(x>>36)-(t<x); return (Q[j]=t-x); } #define CNG (… Continue reading source code of udgraph_solver301a dot c

#include <stdio.h> int main(void) { int hex; unsigned char car; int val; int done; FILE *in; done = 0; in = fopen(“/home/david/graphs/golomb5/hexdumpdotc2/hexdump02a.txt”, “r”); while( done == 0) { val = fscanf(in, “%x”, &hex); if(val == EOF) { done = 1; } if(done == 0) { car = (unsigned char) hex; printf(“%c”, car); } } return… Continue reading source code of aitch eee exx restore02a dot c

#include <stdio.h> int main(void) { int j; int ch; int done; FILE *in; done = 0; j = 0; in = fopen(“/home/david/graphs/golomb5/hexdumpdotc/abbyspeech01a.txt”, “r”); while( done == 0) { ch = fgetc(in); if(ch == EOF) { done = 1; } if(done == 0) { j = j+1; printf(“%02x “, ch); if(0 == (j%16)) { printf(“\n”); }… Continue reading source code of aitch eee exx dump02a dot c

20 46 6f 75 72 20 73 63 6f 72 65 20 61 6e 64 20 73 65 76 65 6e 20 79 65 61 72 73 20 61 67 6f 20 6f 75 72 20 66 61 74 68 65 72 73 20 62 72 6f 75 67 68 74 20 66 6f 72… Continue reading Result of running hexdump02a.out on famous text…

In 2013, I wrote a program to search for unit distance graphs with as many edges as possible, for the number of vertices, and that take 4 colors to color the vertices so that vertices connected by an edge are colored differently. In a unit distance graph, or rather its embedding in the plane, all… Continue reading Sketch of 10-vertex unit distance graph, 2013