62 lines
3.5 KiB
XML
62 lines
3.5 KiB
XML
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 280 280" role="img" aria-labelledby="mark-title-near-critical">
|
|
<title id="mark-title-near-critical">A radius-2 ball in the 3-regular tree with a soft circumscribing arc, above a horizontal threshold ruler marking the near-critical whisker between log B_h and log B_h minus 2 log log B_h minus W_h</title>
|
|
<desc>A frontispiece mark for "Near-Critical First-Moment Lower Bounds for Growing-Radius Domination in Random Regular Graphs." The central figure is a radius-2 ball in the 3-regular tree — root at the bottom, three children at the first level, six grandchildren at the second level (B_2 = 10 for d=3), enclosed by a soft circumscribing arc. Above the ball, a horizontal ruler runs from left to right with two calibrated tick marks: the leftmost tick at the theorem's reachable coordinate log B_h - 2 log log B_h - W_h, and the rightmost tick at the predicted critical coordinate log B_h. Between them, a small horizontal bracket marks the diverging whisker W_h — the bounded critical window the theorem cannot close. The mark says: here is the ball, here is where the theorem stops, and here is what remains open.</desc>
|
|
|
|
<circle cx="140" cy="140" r="128" stroke="currentColor" stroke-width="0.6" fill="none"/>
|
|
|
|
<g stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round">
|
|
<line x1="140" y1="196" x2="102" y2="176" stroke-width="1.0"/>
|
|
<line x1="140" y1="196" x2="140" y2="170" stroke-width="1.0"/>
|
|
<line x1="140" y1="196" x2="178" y2="176" stroke-width="1.0"/>
|
|
|
|
<line x1="102" y1="176" x2="82" y2="150" stroke-width="0.8"/>
|
|
<line x1="102" y1="176" x2="112" y2="146" stroke-width="0.8"/>
|
|
<line x1="140" y1="170" x2="126" y2="140" stroke-width="0.8"/>
|
|
<line x1="140" y1="170" x2="154" y2="140" stroke-width="0.8"/>
|
|
<line x1="178" y1="176" x2="168" y2="146" stroke-width="0.8"/>
|
|
<line x1="178" y1="176" x2="198" y2="150" stroke-width="0.8"/>
|
|
</g>
|
|
|
|
<g fill="currentColor" stroke="none">
|
|
<circle cx="140" cy="196" r="2.4"/>
|
|
|
|
<circle cx="102" cy="176" r="1.7"/>
|
|
<circle cx="140" cy="170" r="1.7"/>
|
|
<circle cx="178" cy="176" r="1.7"/>
|
|
|
|
<circle cx="82" cy="150" r="1.3"/>
|
|
<circle cx="112" cy="146" r="1.3"/>
|
|
<circle cx="126" cy="140" r="1.3"/>
|
|
<circle cx="154" cy="140" r="1.3"/>
|
|
<circle cx="168" cy="146" r="1.3"/>
|
|
<circle cx="198" cy="150" r="1.3"/>
|
|
</g>
|
|
|
|
<path
|
|
d="M 70 152 Q 70 128 90 118 Q 120 108 140 108 Q 160 108 190 118 Q 210 128 210 152"
|
|
stroke="currentColor" stroke-width="0.5" fill="none" stroke-linecap="round"
|
|
stroke-dasharray="3 2" opacity="0.55"/>
|
|
|
|
<line x1="52" y1="72" x2="228" y2="72" stroke="currentColor" stroke-width="0.9" stroke-linecap="round"/>
|
|
|
|
<g stroke="currentColor" fill="none" stroke-linecap="round" stroke-width="0.9">
|
|
<line x1="102" y1="66" x2="102" y2="78"/>
|
|
<line x1="212" y1="66" x2="212" y2="78"/>
|
|
</g>
|
|
|
|
<circle cx="102" cy="72" r="2.0" fill="currentColor" stroke="none"/>
|
|
<circle cx="212" cy="72" r="2.0" stroke="currentColor" stroke-width="0.9" fill="none"/>
|
|
|
|
<g stroke="currentColor" fill="none" stroke-linecap="round" stroke-width="0.7">
|
|
<line x1="102" y1="52" x2="212" y2="52"/>
|
|
<line x1="102" y1="49" x2="102" y2="55"/>
|
|
<line x1="212" y1="49" x2="212" y2="55"/>
|
|
</g>
|
|
|
|
<g stroke="currentColor" fill="none" stroke-linecap="round" stroke-width="0.5" opacity="0.7">
|
|
<line x1="140" y1="49" x2="140" y2="55"/>
|
|
<line x1="176" y1="49" x2="176" y2="55"/>
|
|
</g>
|
|
|
|
</svg>
|