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#extremalcombinatorics

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Ross Kang<p>Just yesterday, I was musing to a (younger) research visitor, "I hope that within my lifetime we will still see another breakthrough on the bounds for R(3,k)"...</p><p><a href="https://arxiv.org/abs/2505.13371" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2505.13371</span><span class="invisible"></span></a></p><p>I am excited to see what developments follow on from here!</p><p>(Also that old adage: just as soon as you publish a survey (<a href="https://arxiv.org/abs/2501.03379" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2501.03379</span><span class="invisible"></span></a>) it is out of date.)</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/ExtremalCombinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ExtremalCombinatorics</span></a> <a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>probability</span></a></p>
Ross Kang<p>For various (mathematical, meteorological, alimentary) reasons, I usually prefer 2π day.<br>Nevertheless, today I make the following offering:</p><p><a href="http://arxiv.org/abs/2503.10002" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="">arxiv.org/abs/2503.10002</span><span class="invisible"></span></a></p><p>Pjotr Buys, <span class="h-card" translate="no"><a href="https://mathstodon.xyz/@Janvadehe" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>Janvadehe</span></a></span> and I used Shearer's induction to address the question:</p><p>How few independent sets can a triangle-free graph of average degree d have?</p><p> <br>The answer is close to how many a random graph has.<br>What is perhaps surprising is just *how* close it comes.<br>(I queried the combinatorial hive mind about this last week.)</p><p><a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <a href="https://mathstodon.xyz/tags/ExtremalCombinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ExtremalCombinatorics</span></a> <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>probability</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/piDay" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>piDay</span></a></p>
Ross Kang<p>Starting out in mathematical research, especially in discrete mathematics, a big focus is problem-solving. It's like a race, and once you've solved one, you set out right away for the next adrenaline rush.</p><p>Take for granted a bustling market of open problems (again, especially in discrete mathematics). Scour papers or problem sites. Challenge close colleagues with the ones that eluded you. The harder, the better, right? There is occasionally awkward coffee talk of that intangible `taste' or `judgement', but, come on, less talk and more solving!</p><p>(please imagine here a subtly ironic tone in my voice)</p><p>(1/3)</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <br><a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <br><a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <br><a href="https://mathstodon.xyz/tags/ExtremalCombinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ExtremalCombinatorics</span></a></p>
Ross Kang<p>A post of <span class="h-card" translate="no"><a href="https://mathstodon.xyz/@11011110" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>11011110</span></a></span> has reminded me that (after a year and a half lurking here) it's never too late for me to toot and pin an intro here.</p><p>I am a Canadian mathematician in the Netherlands, and I have been based at the University of Amsterdam since 2022. I also have some rich and longstanding ties to the UK, France, and Japan.</p><p>My interests are somewhere in the nexus of Combinatorics, Probability, and Algorithms. Specifically, I like graph colouring, random graphs, and probabilistic/extremal combinatorics. I have an appreciation for randomised algorithms, graph structure theory, and discrete geometry.</p><p>Around 2020, I began taking a more active role in the community, especially in efforts towards improved fairness and openness in science. I am proud to be part of a team that founded the journal, Innovations in Graph Theory (<a href="https://igt.centre-mersenne.org/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">igt.centre-mersenne.org/</span><span class="invisible"></span></a>), that launched in 2023. (That is probably the main reason I joined mathstodon!) I have also been a coordinator since 2020 of the informal research network, A Sparse (Graphs) Coalition (<a href="https://sparse-graphs.mimuw.edu.pl/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">sparse-graphs.mimuw.edu.pl/</span><span class="invisible"></span></a>), devoted to online collaborative workshops. In 2024, I helped spearhead the MathOA Diamond Open Access Stimulus Fund (<a href="https://www.mathoa.org/diamond-open-access-stimulus-fund/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">mathoa.org/diamond-open-access</span><span class="invisible">-stimulus-fund/</span></a>).</p><p>Until now, my posts have mostly been about scientific publishing and combinatorics.</p><p><a href="https://mathstodon.xyz/tags/introduction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>introduction</span></a> <br><a href="https://mathstodon.xyz/tags/openscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>openscience</span></a> <br><a href="https://mathstodon.xyz/tags/diamondopenaccess" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>diamondopenaccess</span></a> <br><a href="https://mathstodon.xyz/tags/scientificpublishing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>scientificpublishing</span></a> <br><a href="https://mathstodon.xyz/tags/openaccess" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>openaccess</span></a> <br><a href="https://mathstodon.xyz/tags/RemoteConferences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>RemoteConferences</span></a> <br><a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <br><a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <br><a href="https://mathstodon.xyz/tags/ExtremalCombinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ExtremalCombinatorics</span></a> <br><a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>probability</span></a></p>