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Remark on disconnected graphs.
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1 % TeX macros for typesetting my PhD thesis
2 % (c) 2008 Martin Mares <mj@ucw.cz>
3
4 \input epsf.tex
5 \input btxmac.tex
6 \input amssym.tex
7
8 \catcode`@=11
9
10 %%% Basic parameters %%%
11
12 % A4 with 1in margins, leaving 20pt for page numbering at the bottom
13 \hsize=159mm
14 \vsize=246mm
15 \advance\vsize by -20pt
16 \parindent=0.8cm
17 \parskip=3pt plus 1pt minus 1pt
18
19 \smallskipamount=4pt plus 1.2pt minus 1.2pt
20 \medskipamount=7pt plus 2.5pt minus 2pt
21 \bigskipamount=15pt plus 5pt minus 4pt
22
23 \abovedisplayskip=15pt plus 4pt minus 10pt
24 \abovedisplayshortskip=0pt plus 3pt
25 \belowdisplayskip=15pt plus 4pt minus 10pt
26 \belowdisplayshortskip=8.5pt plus 3.5pt minus 4.5pt
27
28 %%% Miscellanea %%%
29
30 \def\em#1{{\it #1\/}}
31 \def\df#1{{\it #1\/}}   % when we define something
32 \def\O{{\cal O}}
33 \def\<#1>{\leavevmode\hbox{\it #1\/}}
34 \let\>=\noindent
35 \def\qed{{\parfillskip=0pt\allowbreak\hfill\nobreak $\spadesuit$\par}}
36 \def\qeditem{{\parfillskip=0pt\hfill\rlap{\hskip\rightskip\llap{$\spadesuit$}}\par}}
37 \def\qedmath{\eqno{\spadesuit}}
38 \def\FIXME#1{\>{\bo TODO:} #1}
39 \def\symdiff{\mathbin{\Delta}}
40 \def\rack#1#2{\setbox0=\hbox{#1}\hbox to \wd0{#2}}
41 \def\o#1{\accent23 #1}
42 \def\mst{\mathop{\rm mst}}
43 \def\deg{\mathop{\rm deg}}
44 \def\timesalpha{\mskip2mu\alpha}
45 \def\timesbeta{\mskip2mu\beta}
46 \def\tower{\mathop\uparrow}
47 \def\Forb{{\rm Forb}}
48 \def\minorof{\preccurlyeq}
49 \def\per{\mathop{\rm per}}
50 \def\poly{\mathop{\rm poly}}
51
52 % Bit strings
53 \def\0{{\bf 0}}
54 \def\1{{\bf 1}}
55 \def\(#1){\mathord{\left<#1\right>}}
56
57 % Bitwise operations
58 \def\shl{\mathbin{<\!<}}
59 \def\shr{\mathbin{>\!>}}
60 \def\bop#1{\mathbin{\hbox{\sc #1}}}
61 \def\band{\bop{and}}
62 \def\bor{\bop{or}}
63 \def\bxor{\bop{xor}}
64 \def\bnot{\mathop{\hbox{\sc not}}}
65
66 % A reversed version of \ddots with extra space at the top to get good alignment of exponents.
67 \def\rddots{\mathinner{\mkern1mu\raise\p@\vbox{\kern7\p@\hbox{.}}\mkern2mu
68     \raise4\p@\hbox{.}\mkern2mu\raise7\p@\hbox{.}\raise11\p@\hbox{}\mkern1mu}}
69
70 % Footnotes
71 \newcount\footcnt
72 \footcnt=0
73 \def\foot#1{\global\advance\footcnt by 1{\parindent=0.25in\parskip=0pt\footnote{$^{\bf\the\footcnt}$}{#1}}}
74
75 %%% Fonts %%%
76
77 \font\twelverm=cmr12
78 \font\twelveit=cmti12
79 \font\twelvebf=cmbx12
80
81 %\font\twelverm=pplr8z at 12pt
82 %\font\twelveit=pplri8z at 12pt
83 %\font\twelvebf=pplb8z at 12pt
84
85 \font\twelvesl=cmsl12
86 \font\twelveb=cmb12
87 \font\twelvesc=cmcsc12
88
89 \def\mathf@nt#1#2#3#4{%
90 \toks0=\expandafter{\csname#1#2\endcsname}%
91 \expandafter\ifx\the\toks0\relax%
92 %\immediate\write-1{bb \the\toks0=#4#2#3}%
93 \global\expandafter\font\the\toks0=#4#2#3%
94 \fi%
95 \edef\m@@f{\the\toks0}}
96
97 \def\fntmathsize{12}
98 \def\fntmathtok{twelve}
99 \def\fntmathssize{8}
100 \def\fntmathstok{eight}
101 \def\fntmathsssize{6}
102 \def\fntmathsstok{six}
103
104 \mathf@nt{\fntmathtok}{r}{\fntmathsize}{cm}\textfont0=\m@@f
105 \mathf@nt{\fntmathstok}{r}{\fntmathssize}{cm}\scriptfont0=\m@@f
106 \mathf@nt{\fntmathsstok}{r}{\fntmathsssize}{cm}\scriptscriptfont0=\m@@f
107 \mathf@nt{\fntmathtok}{mi}{\fntmathsize}{cm}\skewchar\m@@f='177\textfont1=\m@@f
108 \mathf@nt{\fntmathstok}{mi}{\fntmathssize}{cm}\skewchar\m@@f='177\scriptfont1=\m@@f
109 \mathf@nt{\fntmathsstok}{mi}{\fntmathsssize}{cm}\skewchar\m@@f='177\scriptscriptfont1=\m@@f
110 \mathf@nt{\fntmathtok}{sy}{\fntmathsize}{cm}\skewchar\m@@f='60\textfont2=\m@@f
111 \mathf@nt{\fntmathstok}{sy}{\fntmathssize}{cm}\skewchar\m@@f='60\scriptfont2=\m@@f
112 \mathf@nt{\fntmathsstok}{sy}{\fntmathsssize}{cm}\skewchar\m@@f='60\scriptscriptfont2=\m@@f
113 \mathf@nt{\fntmathtok}{ex}{\fntmathsize}{cm}\textfont3=\m@@f\scriptfont3=\m@@f\scriptscriptfont3=\m@@f
114 \mathf@nt{\fntmathtok}{ti}{\fntmathsize}{cm}\textfont\itfam=\m@@f
115 \mathf@nt{\fntmathtok}{sl}{\fntmathsize}{cm}\textfont\slfam=\m@@f
116 \mathf@nt{\fntmathtok}{bx}{\fntmathsize}{cm}\textfont\bffam=\m@@f
117 \mathf@nt{\fntmathtok}{tt}{\fntmathsize}{cm}\hyphenchar\m@@f=-1\textfont\ttfam=\m@@f
118 \mathf@nt{\fntmathtok}{msam}{\fntmathsize}{}\textfont\msafam=\m@@f
119 \mathf@nt{\fntmathstok}{msam}{\fntmathssize}{}\scriptfont\msafam=\m@@f
120 \mathf@nt{\fntmathsstok}{msam}{\fntmathsssize}{}\scriptscriptfont\msafam=\m@@f
121 \mathf@nt{\fntmathtok}{msbm}{\fntmathsize}{}\textfont\msbfam=\m@@f
122 \mathf@nt{\fntmathstok}{msbm}{\fntmathssize}{}\scriptfont\msbfam=\m@@f
123 \mathf@nt{\fntmathsstok}{msbm}{\fntmathsssize}{}\scriptscriptfont\msbfam=\m@@f
124
125 % Blackboard bold font
126 \newfam\bbfam
127 \font\bbtwelve=bbm12
128 \font\bbeight=bbm8
129 \font\bbsix=bbm6
130 \textfont\bbfam=\bbtwelve
131 \scriptfont\bbfam=\bbeight
132 \scriptscriptfont\bbfam=\bbsix
133 \def\bb{\bbtwelve\fam\bbfam}
134
135 % Font switches
136 \def\rm{\fam\z@\twelverm}
137 \def\it{\fam\itfam\twelveit}
138 \def\bo{\fam\bffam\twelveb}
139 \def\bf{\fam\bffam\twelvebf}
140 \def\tt{\fam\ttfam\twelvett\hyphenchar\twelvett=-1\relax}
141 \def\sc{\twelvesc}
142 \def\sl{\fam\slfam\twelvesl}
143
144 % Switch to 12pt baselines
145 \rm
146 \baselineskip=14.4pt
147 \lineskip=1.2pt
148 \setbox\strutbox=\hbox{\vrule height 10.2pt depth 4.2pt width 0pt}
149
150 % Other fonts
151 \font\chapfont=csssdc17 scaled \magstep1
152 \font\secfont=csb14
153 \font\secitfont=csbxti14
154
155 %%% FIXME
156 \footline={\hss\twelverm\folio\hss}
157
158 %%% Enumerated lists %%%
159
160 \newif\ifitem\itemtrue
161 \newbox\itembox
162 \newcount\itemcount
163
164 \def\interlistskip{\vskip 3pt plus 2pt minus 1pt}
165
166 \def\itemspacingrules{\ifitem\advance\leftskip by \parindent\parindent=0pt\itemfalse\else
167 \advance\leftskip by 2.5em\fi\rightskip=\leftskip}
168
169 \def\inititemize{\interlistskip\begingroup
170 \parskip=1pt plus 0.3pt minus 0.1pt
171 \itemspacingrules}
172
173 \def\itemize#1{\inititemize\setbox\itembox\llap{#1\hskip 0.4em}%
174 \let\:=\singleitem}
175
176 \def\singleitem{\par\leavevmode\copy\itembox}
177
178 \def\endlist{\interlistskip\endgroup}
179
180 \def\ibull{\raise0.2ex\hbox{$\bullet$}} % Signs frequently used for \itemize
181 \def\idot{\raise0.2ex\hbox{$\cdot$}}
182 \def\istar{\raise0.2ex\hbox{$\ast$}}
183
184 \def\numlist#1{\inititemize\itemcount=0\let\:=\numbereditem
185 \let\itemnumbering=#1}
186
187 \def\numbereditem{\par\leavevmode\advance\itemcount by 1
188 \llap{\itemnumbering\hskip 0.4em}}
189
190 \def\nnorm{\the\itemcount}
191 \def\ndotted{\nnorm.}
192 \def\nparen{\nnorm)}
193 \def\nroman{\romannumeral\itemcount}
194 \def\nromanp{\nroman)}
195 \def\nalpha{\count@=96\advance\count@ by\itemcount\char\count@)}
196 \def\nAlpha{\count@=64\advance\count@ by\itemcount\char\count@)}
197 \def\ngreek{$\ifcase\itemcount\or\alpha\or\beta\or\gamma\or\delta\or\epsilon\or
198 \zeta\or\eta\or\theta\or\iota\or\kappa\or\lambda\or\mu\or\nu\or\xi\or\pi\or\rho
199 \or\sigma\or\tau\or\upsilon\or\phi\or\chi\or\psi\or\omega\fi$)}
200
201 % New \frenchspacing, which doesn't leave unwanted spaces in text.
202 \def\frenchsp@cing{\sfcode`\.\@m \sfcode`\?\@m \sfcode`\!\@m%
203 \sfcode`\:\@m \sfcode`\;\@m \sfcode`\,\@m}
204
205 %%% Local verbatim mode %%%
206
207 \def\make@ther#1{\catcode`#1=12\relax}
208 \def\setverb@tim{\tt\frenchsp@cing\catcode`\`=13\catcode`\'=13\n@ligs%
209 \let\do=\make@ther\dospecials\obeyspaces}
210
211 {\catcode`'=13
212 \catcode``=13
213 \gdef\n@ligs{\def`{\relax\lq}\def'{\relax\rq}}}
214
215 {\obeyspaces
216 \global\chardef\sp@ce=32
217 \gdef\showspaces{\let =\sp@ce}
218 \global\let =\ }
219
220 \catcode124=\active % Make | active
221 \def\ttst@rt{\begingroup\setverb@tim\let|=\endgroup}
222 \let|=\ttst@rt
223
224 %%% Verbatim mode for text in { } %%%
225
226 \newskip\verbglue\newskip\verblineglue
227 \verbglue=3pt plus 1pt minus 0.3pt
228 \verblineglue=0pt plus 1.5pt
229 \def\verblocaldefs{}
230
231 \newdimen\tabwidth
232 \newcount\tabsize
233 \tabsize=8
234 \newdimen\t@b
235
236 \newcount\vercnt
237 \def\v@rbend{\par\endgroup\vskip\verbglue}
238 \def\v@rbl{\ifnum\vercnt>0\{\fi\global\advance\vercnt by 1\relax}
239 \def\v@rbr{\ifnum\vercnt>1\}\else\v@rbend\fi\global\advance\vercnt by -1\relax}
240 \def\v@rbparams{\setverb@tim\parskip=\verblineglue\parindent=0pt\raggedbottom%
241 \rightskip\z@ plus1fil\pretolerance=10000\tolerance=10000\vercnt=0%
242 \catcode124=12\setupt@bs\vskip\verbglue\defb@x\obeylines}
243
244 \def\startb@x{\setbox0=\hbox\bgroup}
245 \def\defb@x{\def\par{\leavevmode\egroup\box0\endgraf}%
246 \everypar{\startb@x}}
247
248 {\catcode`\^^I=\active
249 \gdef\setupt@bs{\catcode`\^^I=\active
250 \setbox0=\hbox{\tt\ }\tabwidth=\wd0\multiply\tabwidth by \tabsize
251 \def^^I{\leavevmode\egroup\t@b=\wd0\divide\t@b by \tabwidth%
252 \multiply\t@b by \tabwidth%
253 \advance\t@b by \tabwidth\advance\t@b by -\wd0\box0\hbox to \t@b{}\startb@x}
254 }}
255
256 {
257 \catcode`[=1\catcode`]=2\catcode123=\active\catcode125=\active
258 \gdef\verbatim[\begingroup\v@rbparams\catcode123=\active\catcode125=\active%
259 \let{=\v@rbl\let}=\v@rbr\chardef\{=123\chardef\}=125\verblocaldefs
260 ]]
261
262 \def\verbinput#1{\begingroup\v@rbparams\input #1\endgroup}
263
264 %%% Algorithms %%%
265
266 %       \algo{jmeno algoritmu}
267 %       \algin popis vstupu
268 %       \:krok
269 %       \:krok
270 %       \::vnoreny krok
271 %       \algout popis vystupu
272 %       \endalgo
273
274 \def\algo{
275 \interlistskip
276 \begingroup
277 \let\:=\algoitem
278 \parskip=1pt plus 1pt minus 0.3pt
279 \rightskip=2em
280 \itemcount=0
281 \smallskip
282 }
283 \def\endalgo{\interlistskip\endgroup}
284 \def\algopar{\par
285 \parindent=2em
286 \hangindent=4em
287 \hangafter=1
288 \leavevmode
289 }
290 \def\algoitem{
291 \algopar\advance\itemcount by 1
292 \hbox to 2em{\hss \the\itemcount. }%
293 \futurelet\next\algoitemh}
294 \def\algoitemh{\ifx\next:\let\next=\algohang\else\let\next=\relax\fi\next}
295 \def\algohang:{\advance\hangindent by 2em \hskip 2em\futurelet\next\algoitemh}
296 \def\algin{\par{\sl Input:\/} }
297 \def\algout{\par{\sl Output:\/} }
298
299 %%% Constructs used in algorithms %%%
300
301 \def\={\leftarrow}
302 \def\cmt#1{~~{\sl (#1)}}
303
304 %%% Chapters, sections and proclamations %%%
305
306 \newcount\chapcount
307 \newcount\seccount
308 \newcount\thmcount
309 \chapcount=0
310 \seccount=0
311 \thmcount=0
312 \def\currentid{??}
313
314 \def\chapter#1{\vfill\supereject
315 \advance\chapcount by 1
316 \seccount=0
317 \thmcount=0
318 \footcnt=0
319 \edef\currentid{\the\chapcount}
320 \leftline{\chapfont\currentid. #1}
321 \bigskip
322 }
323
324 \def\section#1{\bigskip
325 \advance\seccount by 1
326 \thmcount=0
327 \edef\currentid{\the\chapcount.\the\seccount}
328 \leftline{\secfont\currentid. #1}
329 \medskip
330 }
331
332 \def\para{\advance\thmcount by 1
333 \edef\currentid{\the\chapcount.\the\seccount.\the\thmcount}
334 \noindent {\bo \currentid.\enspace}}
335
336 \def\proclaim#1{\para {\bo #1.\enspace}}
337
338 \def\thm{\proclaim{Theorem}}
339 \def\lemma{\proclaim{Lemma}}
340 \def\defn{\proclaim{Definition}}
341 \def\problem{\proclaim{Problem}}
342 \def\obs{\proclaim{Observation}}
343 \def\rem{\proclaim{Remark}}
344 \def\alg{\proclaim{Algorithm}}
345 \def\impl{\proclaim{Implementation}}
346 \def\cor{\proclaim{Corollary}}
347 \def\nota{\proclaim{Notation}}
348 \def\example{\proclaim{Example}}
349
350 \def\label#1{{\sl (#1)\/}\enspace}
351 \def\labelx#1{\label{#1}\hfil\break\kern 0pt}   % Eat spaces
352
353 \def\thmn{\thm\labelx}
354 \def\lemman{\lemma\labelx}
355 \def\defnn{\defn\labelx}
356 \def\corn{\cor\labelx}
357 \def\algn{\alg\label}
358 \def\notan{\nota\labelx}
359 \def\examplen{\example\labelx}
360 \def\problemn{\problem\labelx}
361 \def\remn{\rem\labelx}
362
363 \def\paran#1{\para {\sl #1:}}
364
365 \def\proof{\noindent {\sl Proof.}\enspace}
366 \def\proofsketch{\noindent {\sl Proof sketch.}\enspace}
367
368 %%% References %%%
369
370 \newwrite\ids
371 \def\writeid#1#2{\immediate\write\ids{\string\def\expandafter\string\csname id#1\endcsname{#2}}}
372
373 \immediate\openin\ids=\jobname.ids
374 \ifeof\ids
375 \else
376 \input \jobname.ids
377 \fi
378 \immediate\closein\ids
379 \immediate\openout\ids=\jobname.ids
380
381 \def\ref#1{\expandafter\ifx\csname id#1\endcsname\relax
382 {\bo ??}%
383 \immediate\write16{*** Warning: Reference #1 undefined ***}%
384 \else
385 \csname id#1\endcsname
386 \fi
387 }
388
389 \def\id#1{\writeid{#1}{\currentid}}
390
391 %%% Bibliography %%%
392
393 %\bibliographystyle{abbrv}
394 \bibliographystyle{alpha}
395 \def\dumpbib{
396   \def\bblhook{\parskip=2pt plus 1pt minus 0.5pt}
397   \bibliography{biblio}
398 }
399
400 %%% Figures %%%
401
402 \def\figure#1#2#3{\midinsert
403 \medskip
404 \centerline{\epsfxsize=#2\epsfbox{pic/#1}}
405 \medskip
406 \smallskip
407 \centerline{#3}
408 \endinsert}
409
410 %%% Stand-alone chapters %%%
411
412 \def\endpart{
413   \section{Bibliography}
414   \dumpbib
415   \vfill\supereject\end
416 }
417
418 %%% The End %%%
419
420 \catcode`@=12