Tootfinder

Single conflict coloring, adaptable choosability and separation choosability
Carl Johan Casselgren, Kalle Eriksson
https://arxiv.org/abs/2509.13913 https://

Single conflict coloring, adaptable choosability and separation choosability
We study relations between three interrelated notions of graph (list) coloring: single conflict coloring, adapted list coloring and choosability with separation (with $1$ overlapping color between lists of adjacent vertices), and their respective invariants single conflict chromatic number $χ_{\nleftrightarrow}$, adaptable choosability $ch_{ad}$ and separation choosability $ch_{sep}$. We investigate graphs with small values of these invariants, and construct explicit families of graphs $G$ wit…

🇺🇦 #NowPlaying on BBCRadio3's #NightTracks
Claire M Singer:
🎵 Braeriach
#ClaireMSinger
https://open.spotify.com/track/4Bl4Y2JgtcOmlXnIj1YtpL
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Wall Street clearinghouse DTCC selects the Canton Network blockchain as a real-world asset tokenization partner after receiving a No-Action Letter from the SEC (Ian Allison/CoinDesk)
https://www.coindesk.com/business/2025/12/

Wall Street giant DTCC Picks privacy focused blockchain Canton Network for tokenization
Canton creator Digital Asset will help tokenize DTC-custodied U.S. Treasury securities.

A counterexample to the $S_{10}$- and the $S_{12}$-Conjecture
Isaak H. Wolf
https://arxiv.org/abs/2509.14184 https://arxiv.org/pdf/2509.14184

A counterexample to the $S_{10}$- and the $S_{12}$-Conjecture
For two graphs $G$ and $H$, a mapping $f\colon E(G) \to E(H)$ is an $H$-coloring of $G$, if it is a proper edge-coloring and for every $v \in V(G)$ there exists a vertex $u \in V(H)$ with $f(\partial_G(v))=\partial_H(u)$. Motivated by the Petersen Coloring Conjecture, Mkrtchyan [A remark on the Petersen coloring conjecture of Jaeger, \emph{Australas. J. Combin.}, 56 (2013), 145-151] and Mkrtchyan together with Hakobyan [$S_{12}$ and $P_{12}$-colorings of cubic graphs, \emph{Ars Math. Contemp.},…

Happening now in the waiting room at the music store where Kid2 to takes lessons: a kid who's maybe 4 coloring while belting out Bowie's "Starman" as loud as possible.

Now that's a Russian response to protests. But it's coming or of Portland
https://www.independent.co.uk/news/world/americas/crime/portland-ice-clarinet-arrested-protest-b2845329.html

Musician playing ‘Ghostbusters’ outside ICE facility is arrested by agents: ‘Why are they targeting a clarinetist?’
‘Taking us citizens out of state to detain them without charge is a new action from the Feds and should be opposed,’ her band said

lmao
https://skyview.social/?url=https:%2F/bsky.app/profile/did:plc:nx2hxdrsv3mivqwwvkq7xlqx/post/3ma7gyvkyjk24&viewtype=tree

"Biodiversity loss due to land use change could be highly underestimated: Study"
#Animals #Biodiversity

Biodiversity loss due to land use change could be highly underestimated: Study
A survey of Colombian birdlife, which evolved over more than a decade into the world’s largest-ever ornithological study, has found that clearing forests to create new pastures is causing as much as 60% more damage to biodiversity than previously thought. Until now, research into the impact on biodiversity of land use change has generally involved […]

#Madagascar : avant de choisir les personnes, il faut que la direction, la méthodologie et le calendrier soient clairement définis.
Et franchement, dans quelle mesure peut-on faire confiance pour le choix d'un Premier ministre Š des députés qui ont avant tout démontré leur versatilité et qui, plutôt que de défendre des idées, défendent prioritairement leurs fauteuils et tickets carburan…

Structure, Perfect Divisibility and Coloring of ($P_2\cup P_4, C_3$)-Free Graphs
Ran Chen, Di Wu, Xiaowen Zhang
https://arxiv.org/abs/2509.14135 https://ar…

Structure, Perfect Divisibility and Coloring of ($P_2\cup P_4, C_3$)-Free Graphs
Randerath {\em et al.} [Discrete Math. 251 (2002) 137-153] proved that every $(P_6,C_3)$-free graph $G$ satisfies $χ(G)\leq4$. Pyatkin [Discrete Math. 313 (2013) 715-720] proved that every $(2P_3,C_3)$-free graph $G$ satisfies $χ(G)\leq4$. In this paper, we prove that for a connected $(P_2\cup P_4, C_3)$-free graph $G$, either $G$ has two nonadjacent vertices $u,v$ such that $N(u)\subseteq N(v)$, or $G$ is 3-colorable, or $G$ contains Grőtzsch graph as an induced subgraph and is an induced s…