# Fdb version 3 ["pdflatex"] 1779726421 "paper.tex" "paper.pdf" "paper" 1779726423 "/usr/local/texlive/2022/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmbsy5.tfm" 1246382020 1120 1e8878807317373affa7f7bba4cf2f6a "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmbsy6.tfm" 1246382020 1124 14ccf5552bc7f77ca02a8a402bea8bfb "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmbsy9.tfm" 1246382020 1112 cbc11b646ccc26599775160605aaee3a "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex9.tfm" 1246382020 996 a18840b13b499c08ac2de96a99eda4bc "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmmib5.tfm" 1246382020 1496 c79f6914c6d39ffb3759967363d1be79 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmmib6.tfm" 1246382020 1516 a3bf6a5e7ec4401b1f52092dfaaed242 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmmib9.tfm" 1246382020 1528 159d57adcba064aab4277245c826577d "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1246382020 916 f87d7c45f9c908e672703b83b72241a3 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm" 1246382020 924 9904cf1d39e9767e7a3622f2a125a565 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1246382020 928 2dc8d444221b7a635bb58038579b861a "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1246382020 908 2921f8a10601f252058503cc6570e581 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm" 1246382020 940 75ac932a52f80982a9f8ea75d03a34cf "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1246382020 940 228d6584342e91276bf566bcf9716b83 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm" 1136768653 1328 c834bbb027764024c09d3d2bf908b5f0 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx5.tfm" 1136768653 1332 f817c21a1ba54560425663374f1b651a "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx6.tfm" 1136768653 1344 8a0be4fe4d376203000810ad4dc81558 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx8.tfm" 1136768653 1332 1fde11373e221473104d6cc5993f046e "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx9.tfm" 1136768653 1328 5442e22a7072966dbaf88ca900acf3f0 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbxti10.tfm" 1136768653 1532 9162035f4e7176612125649e348e2195 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmcsc10.tfm" 1136768653 1300 63a6111ee6274895728663cf4b4e7e81 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmitt10.tfm" 1136768653 768 2297ad2ac26f37e67f756dad27c77d68 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm" 1136768653 1512 f21f83efb36853c0b70002322c1ab3ad "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm" 1136768653 1520 eccf95517727cb11801f4f1aee3a21b4 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmmi9.tfm" 1136768653 1524 d89e2d087a9828407a196f428428ef4a "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmr6.tfm" 1136768653 1300 b62933e007d01cfd073f79b963c01526 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmr8.tfm" 1136768653 1292 21c1c5bfeaebccffdb478fd231a0997d "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmr9.tfm" 1136768653 1292 6b21b9c2c7bebb38aa2273f7ca0fb3af "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm" 1136768653 1116 933a60c408fc0a863a92debe84b2d294 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1136768653 1120 8b7d695260f3cff42e636090a8002094 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmsy9.tfm" 1136768653 1116 25a7bf822c58caf309a702ef79f4afbb "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmti10.tfm" 1136768653 1480 aa8e34af0eb6a2941b776984cf1dfdc4 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmti7.tfm" 1136768653 1492 86331993fe614793f5e7e755835c31c5 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmti8.tfm" 1136768653 1504 1747189e0441d1c18f3ea56fafc1c480 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmtt10.tfm" 1136768653 768 1321e9409b4137d6fb428ac9dc956269 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmtt9.tfm" 1136768653 764 c98a2af25c99b73a368cf7336e255190 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb" 1248133631 34811 78b52f49e893bcba91bd7581cdc144c0 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx8.pfb" 1248133631 32166 b0c356b15f19587482a9217ce1d8fa67 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx9.pfb" 1248133631 32298 c6d25bb16d1eac01ebdc6d7084126a1e "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbxti10.pfb" 1248133631 36554 b67dc2cfa451409e100b3fcf5f506509 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmcsc10.pfb" 1248133631 32001 6aeea3afe875097b1eb0da29acd61e28 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb" 1248133631 30251 6afa5cb1d0204815a708a080681d4674 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmitt10.pfb" 1248133631 26057 fad158094905eaf20f4ae3782af0c45c "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi6.pfb" 1248133631 37166 8ab3487cbe3ab49ebce74c29ea2418db "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb" 1248133631 36281 c355509802a035cadc5f15869451dcee "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi8.pfb" 1248133631 35469 70d41d2b9ea31d5d813066df7c99281c "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi9.pfb" 1248133631 36094 798f80770b3b148ceedd006d487db67c "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr5.pfb" 1248133631 31809 8670ca339bf94e56da1fc21c80635e2a "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr6.pfb" 1248133631 32734 69e00a6b65cedb993666e42eedb3d48f "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1248133631 32762 224316ccc9ad3ca0423a14971cfa7fc1 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb" 1248133631 32726 0a1aea6fcd6468ee2cf64d891f5c43c8 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr9.pfb" 1248133631 33993 9b89b85fd2d9df0482bd47194d1d3bf3 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy6.pfb" 1248133631 32587 1788b0c1c5b39540c96f5e42ccd6dae8 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb" 1248133631 32716 08e384dc442464e7285e891af9f45947 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb" 1248133631 32626 4f5c1b83753b1dd3a97d1b399a005b4b "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy9.pfb" 1248133631 32442 c975af247b6702f7ca0c299af3616b80 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb" 1248133631 37944 359e864bd06cde3b1cf57bb20757fb06 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb" 1248133631 35660 fb24af7afbadb71801619f1415838111 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10.pfb" 1248133631 31099 c85edf1dd5b9e826d67c9c7293b6786c "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt9.pfb" 1248133631 29078 718ea4567ceff944262b0f5b0800e1d9 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cmextra/cmex8.pfb" 1248133631 30273 87a352d78b6810ae5cfdc68d2fb827b2 "" "/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb" 1248133631 31764 459c573c03a4949a528c2cc7f557e217 "" "/usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1461363279 71627 94eb9990bed73c364d7f53f960cc8c5b "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls" 1591045760 61881 a7369c346c2922a758ae6283cc1ed014 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1359763108 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1359763108 13829 94730e64147574077f8ecfea9bb69af4 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd" 1359763108 961 6518c6525a34feb5e8250ffa91731cff "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd" 1359763108 961 d02606146ba5601b5645f987c92e6193 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1622667781 2222 da905dc1db75412efd2d8f67739f0596 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty" 1622667781 4173 bc0410bcccdff806d6132d3c1ef35481 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty" 1636758526 87648 07fbb6e9169e00cb2a2f40b31b2dbf3c "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty" 1636758526 4128 8eea906621b6639f7ba476a472036bbe "" "/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty" 1636758526 2444 926f379cc60fcf0c6e3fee2223b4370d "" "/usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1579991033 13886 d1306dcf79a944f6988e688c1785f9ce "" "/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1465944070 1224 978390e9c2234eab29404bc21b268d1e "" "/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def" 1601931164 19103 48d29b6e2a64cb717117ef65f107b404 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty" 1622581934 18399 7e40f80366dffb22c0e7b70517db5cb4 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty" 1636758526 7996 a8fb260d598dcaf305a7ae7b9c3e3229 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty" 1622581934 2671 4de6781a30211fe0ea4c672e4a2a8166 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty" 1636758526 4009 187ea2dc3194cd5a76cd99a8d7a6c4d0 "" "/usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def" 1644269979 29921 d0acc05a38bd4aa3af2017f0b7c137ce "" "/usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1279039959 678 4792914a8f45be57bb98413425e4c7af "" "/usr/local/texlive/2022/texmf-dist/web2c/texmf.cnf" 1646502317 40171 cdab547de63d26590bebb3baff566530 "" "/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1647878959 4410336 7d30a02e9fa9a16d7d1f8d037ba69641 "" "/usr/local/texlive/2022/texmf-var/web2c/pdftex/pdflatex.fmt" 1665017617 2826443 7e98410c533054b636c6470db83a27bc "" "/usr/local/texlive/2022/texmf.cnf" 1647878952 577 209b46be99c9075fd74d4c0369380e8c "" "fig_chord_apex_step1.png" 1779497048 128193 2156b95264c4e7be78a47a8f38e36347 "" "fig_chord_apex_step2.png" 1779497048 103549 502d6b9497ab67090f34da927b068fdc "" "fig_chord_apex_step3.png" 1779497048 104380 d3d0e553ec0e4ca7ef3f4de590f42ccb "" "fig_cubic_edge_contraction.png" 1779640620 53219 6cd2c2401c75306080a1dcf52e278eb7 "" "fig_lemma_kempe_heawood.png" 1779675191 63270 cafa66ef29009070323a2dd3229409b0 "" "fig_reduced_dual_step1.png" 1779490218 117795 4da7754ac28df9e809cfa1069e081c53 "" "fig_reduced_dual_step2.png" 1779490218 96839 4f94c996220a2758dd0ff21ebdb9b2be "" "fig_reduced_dual_step3.png" 1779490218 102877 d2a5db5532697441e3150e2ad26b9173 "" "fig_reduced_dual_step4.png" 1779490218 107439 b30c7a68e32660f9bd3a8070bdb96944 "" "fig_thm_cubic_contraction_4face.png" 1779643393 105384 e3682925308ddea06a4f986af1787249 "" "figures/min-face-5-counterexample.png" 1779694886 192060 dd675ae50d32088d97ad647bc6394662 "" "paper.aux" 1779726422 7946 38164e4e6701a73d430f1caa9857e53a "pdflatex" "paper.tex" 1779726385 80516 3cdeee92fefe09fa5794bef1ddc2caf8 "" (generated) "paper.aux" "paper.log" "paper.pdf"