Does Krita require the whole KDE to be installed?

No. Krita needs only kdebase.

Here is the list of packages fetched by Krita Lime when installed on vanilla Ubuntu Trusty with Unity desktop environment. As you see there is only 300MiB of deps, including KDE and Krita itself with all the resources (brushes and stuff).

painter@painter-VirtualBox:~$ sudo sudo apt-get install krita-testing
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following extra packages will be installed:
  consolekit create-resources docbook-xsl icoutils imagemagick-common
  kate-data katepart kde-runtime kde-runtime-data kdelibs-bin kdelibs5-data
  kdelibs5-plugins kdoctools kubuntu-debug-installer libattica0.4
  libbaloocore4 libbaloofiles4 libbalooxapian4 libck-connector0
  libdlrestrictions1 libencode-locale-perl libepub0 libfile-listing-perl
  libfont-afm-perl libgif4 libgsl0ldbl libhtml-form-perl libhtml-format-perl
  libhtml-parser-perl libhtml-tagset-perl libhtml-tree-perl
  libhttp-cookies-perl libhttp-daemon-perl libhttp-date-perl
  libhttp-message-perl libhttp-negotiate-perl libio-html-perl
  libkactivities-bin libkactivities-models1 libkactivities6
  libkatepartinterfaces4 libkcmutils4 libkdcraw-data libkdcraw23
  libkde3support4 libkdeclarative5 libkdecore5 libkdesu5 libkdeui5
  libkdewebkit5 libkdnssd4 libkemoticons4 libkfile4 libkhtml5 libkidletime4
  libkio5 libkjsapi4 libkjsembed4 libkmediaplayer4 libknewstuff3-4
  libknotifyconfig4 libkntlm4 libkparts4 libkpty4 libkrosscore4
  libktexteditor4 libkubuntu0 libkxmlrpcclient4 liblqr-1-0
  liblwp-mediatypes-perl liblwp-protocol-https-perl libmagick++5
  libmagickcore5 libmagickwand5 libnepomuk4 libnepomukcleaner4
  libnepomukcore4abi1 libnepomukquery4a libnepomukutils4 libnet-http-perl
  libntrack-qt4-1 libntrack0 libopencolorio1 libpam-ck-connector libphonon4
  libplasma3 libplot2c2 libpolkit-qt-1-1 libpoppler-qt4-4 libpstoedit0c2a
  libqapt2 libqapt2-runtime libqca2 libqjson0 libqmobipocket1
  libqt4-qt3support libsolid4 libsoprano4 libstreamanalyzer0 libstreams0
  libthreadweaver4 libtinyxml2.6.2 libvirtodbc0 libwww-perl
  libwww-robotrules-perl libxml2-utils libyaml-cpp0.3 libzip2
  nepomuk-core-data nepomuk-core-runtime ntrack-module-libnl-0 odbcinst
  odbcinst1debian2 oxygen-icon-theme phonon phonon-backend-gstreamer
  phonon-backend-gstreamer-common phonon-backend-gstreamer1.0
  plasma-scriptengine-javascript pstoedit qapt-batch shared-desktop-ontologies
  soprano-daemon ttf-dejavu-core virtuoso-minimal virtuoso-opensource-6.1-bin
  virtuoso-opensource-6.1-common
Suggested packages:
  dbtoepub docbook-xsl-doc-html docbook-xsl-doc-pdf docbook-xsl-doc-text
  docbook-xsl-doc docbook-xsl-saxon fop libsaxon-java libxalan2-java
  libxslthl-java xalan libterm-readline-gnu-perl libterm-readline-perl-perl
  djvulibre-bin finger gsl-ref-psdoc gsl-doc-pdf gsl-doc-info gsl-ref-html
  libdata-dump-perl hspell libcrypt-ssleay-perl libmagickcore5-extra
  libqca2-plugin-cyrus-sasl libqca2-plugin-gnupg libqca2-plugin-ossl
  libauthen-ntlm-perl phonon-backend-vlc phonon4qt5-backend-gstreamer xfig
  ivtools-bin tgif transfig
The following NEW packages will be installed:
  consolekit create-resources docbook-xsl icoutils imagemagick-common
  kate-data katepart kde-runtime kde-runtime-data kdelibs-bin kdelibs5-data
  kdelibs5-plugins kdoctools krita-testing kubuntu-debug-installer
  libattica0.4 libbaloocore4 libbaloofiles4 libbalooxapian4 libck-connector0
  libdlrestrictions1 libencode-locale-perl libepub0 libfile-listing-perl
  libfont-afm-perl libgif4 libgsl0ldbl libhtml-form-perl libhtml-format-perl
  libhtml-parser-perl libhtml-tagset-perl libhtml-tree-perl
  libhttp-cookies-perl libhttp-daemon-perl libhttp-date-perl
  libhttp-message-perl libhttp-negotiate-perl libio-html-perl
  libkactivities-bin libkactivities-models1 libkactivities6
  libkatepartinterfaces4 libkcmutils4 libkdcraw-data libkdcraw23
  libkde3support4 libkdeclarative5 libkdecore5 libkdesu5 libkdeui5
  libkdewebkit5 libkdnssd4 libkemoticons4 libkfile4 libkhtml5 libkidletime4
  libkio5 libkjsapi4 libkjsembed4 libkmediaplayer4 libknewstuff3-4
  libknotifyconfig4 libkntlm4 libkparts4 libkpty4 libkrosscore4
  libktexteditor4 libkubuntu0 libkxmlrpcclient4 liblqr-1-0
  liblwp-mediatypes-perl liblwp-protocol-https-perl libmagick++5
  libmagickcore5 libmagickwand5 libnepomuk4 libnepomukcleaner4
  libnepomukcore4abi1 libnepomukquery4a libnepomukutils4 libnet-http-perl
  libntrack-qt4-1 libntrack0 libopencolorio1 libpam-ck-connector libphonon4
  libplasma3 libplot2c2 libpolkit-qt-1-1 libpoppler-qt4-4 libpstoedit0c2a
  libqapt2 libqapt2-runtime libqca2 libqjson0 libqmobipocket1
  libqt4-qt3support libsolid4 libsoprano4 libstreamanalyzer0 libstreams0
  libthreadweaver4 libtinyxml2.6.2 libvirtodbc0 libwww-perl
  libwww-robotrules-perl libxml2-utils libyaml-cpp0.3 libzip2
  nepomuk-core-data nepomuk-core-runtime ntrack-module-libnl-0 odbcinst
  odbcinst1debian2 oxygen-icon-theme phonon phonon-backend-gstreamer
  phonon-backend-gstreamer-common phonon-backend-gstreamer1.0
  plasma-scriptengine-javascript pstoedit qapt-batch shared-desktop-ontologies
  soprano-daemon ttf-dejavu-core virtuoso-minimal virtuoso-opensource-6.1-bin
  virtuoso-opensource-6.1-common
0 upgraded, 128 newly installed, 0 to remove and 12 not upgraded.
Need to get 110 MB of archives.
After this operation, 321 MB of additional disk space will be used.
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