07_interval_labels.ipynb: Minor improvements

Rename some sections, switch which cells belong to which section, move
things around, add some more descriptions, etc.

Author: jnareb

07_interval_labels.ipynb

@@ -32,7 +32,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Spanning tree"
+    "## Definitions: out-tree, spanning tree / tree cover, etc."
    ]
   },
   {
@@ -191,7 +191,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## DFS numbering for DAGs"
+    "## _min-post_ intervals in directed acyclic graphs (DAGs)"
    ]
   },
   {
@@ -362,6 +362,27 @@
     "On the other hand, one can show that $\\tilde{I}_v \\not\\subseteq \\tilde{I}_u \\implies u \\not\\leadsto v$."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Extending _min-post_ intervals for graphs"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This section describes various extensions to the _min-post_ intervals (DFS numbering) going beyond those negative-cut and positive-cut filters described above."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Multiple intervals labelling: GRAIL (TODO)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -511,7 +532,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Computing DFS intervals labelling"
+    "## Visualizing DFS intervals on example graphs"
    ]
   },
   {
@@ -531,19 +552,13 @@
     "TODO"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Examples of spanning trees and min-post tree intervals labelling"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
+    "# this is needed for example (small) graphs\n",
     "import git_commit_graph_ext.example_graphs as graphs"
    ]
   },
@@ -561,7 +576,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Draw a small DAG (from FELINE paper) and its spanning tree, together with _min-post_ tree intervals"
+    "### Examples of spanning trees and min-post tree intervals labelling"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Draw a small DAG (from FELINE paper) and its spanning tree, like on Figure 8 of the FELINE paper, together with its _min-post_ tree intervals."
    ]
   },
   {
@@ -738,6 +760,13 @@
     "  "
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Computing DFS intervals labelling"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},