Tootfinder

Odd list-coloring of graphs of small Euler genus with no short cycles of specific types
Rishi Balaji, Victoria Khazhinsky, Chun-Hung Liu, Kevin Qin
https://arxiv.org/abs/2508.15255

Odd list-coloring of graphs of small Euler genus with no short cycles of specific types
Odd coloring is a variant of proper coloring and has received wide attention. We study the list-coloring version of this notion in this paper. We prove that if $G$ is a graph embeddable in the torus or the Klein bottle with no cycle of length 3, 4, and 6 such that no 5-cycles share an edge, then for every function $L$ that assigns each vertex of $G$ a set $L(v)$ of size 5, there exists a proper coloring that assigns each vertex $v$ of $G$ an element of $L(v)$ such that for every non-isolated ve…

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p-multigrid method for the discontinuous Galerkin discretization of elliptic problems
Nuo Lei, Donghang Zhang, Weiying Zheng
https://arxiv.org/abs/2509.13669 https://

p-multigrid method for the discontinuous Galerkin discretization of elliptic problems
In this paper, we propose a $W$-cycle $p$-multigrid method for solving the $p$-version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems. This SIPDG discretization employs hierarchical Legendre polynomial basis functions. Inspired by the uniform convergence theory of the $W$-cycle $hp$-multigrid method in [P. F. Antonietti, et al., SIAM J. Numer. Anal., 53 (2015)], we provide a rigorous convergence analysis for the proposed $p$-multigrid method, consi…

Spanning path-cycle systems with given end-vertices in regular graphs (full version)
Yoshimi Egawa, Mikio Kano, Kenta Ozeki
https://arxiv.org/abs/2508.11302 https://

Spanning path-cycle systems with given end-vertices in regular graphs (full version)
We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of $G$ such that the distance between any two vertices of $W$ in $G$ is at least 3, $G$ has vertex-disjoint paths and cycles $P_1, \ldots, P_m, C_1, \ldots, C_n$ such that (i) $V(G)=V(P_1) \cup \cdots \cup V(P_m) \cup V(C_1) \cup \cdots \cup V(C_n)$, (ii) each path $P_i$ connects two vertices of $W$, and (iii) the set of…

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🇺🇦 #NowPlaying on #BBC6Music's #LaurenLaverne
Daniel Avery:
🎵 Rapture in Blue (feat. Cecile Believe)
#DanielAvery
https://danielavery.bandcamp.com/track/rapture-in-blue-w-cecile-believe-midnight-version
https://open.spotify.com/track/4VU2zt6DdkIQFGbLCLFIdX

"OOP grew dramatically during the decade between 1985 and 95. The first OOPSLA Conf was held in '86, chaired by Daniel Ingalls of Smalltalk fame. Bjarne Stroustrup released the first versions of C . Brad Cox melted Smalltalk on top of C and created Objective-C. Bertrand Meyer released both Eiffel and his bestseller book. Borland added OOP support to Turbo Pascal 5.5. Famous groups like “The Three Amigos,” “The Gang of Four,” and the Agile movement coalesced around OOP."
…

The Hype Cycle Of OOP
Even though Marketing buzzwords might have an effect akin to Kryptonite against our readers, we're going to use the famous Gartner's Five-Step Hype Cycle to take a closer look at the practice of Object-Oriented Programming (OOP) and its various ups and downs in the past 50 years. Remembering that one of the core tenets of this magazine is to make the impossible dialogue possible, the framework provided by Gartner fits this task perfectly well.

LD-ViCE: Latent Diffusion Model for Video Counterfactual Explanations
Payal Varshney, Adriano Lucieri, Christoph Balada, Sheraz Ahmed, Andreas Dengel
https://arxiv.org/abs/2509.08422

LD-ViCE: Latent Diffusion Model for Video Counterfactual Explanations
Video-based AI systems are increasingly adopted in safety-critical domains such as autonomous driving and healthcare. However, interpreting their decisions remains challenging due to the inherent spatiotemporal complexity of video data and the opacity of deep learning models. Existing explanation techniques often suffer from limited temporal coherence, insufficient robustness, and a lack of actionable causal insights. Current counterfactual explanation methods typically do not incorporate guida…

🇺🇦 #NowPlaying on #BBC6Music's #NickGrimshaw
Daniel Avery:
🎵 Rapture in Blue (feat. Cecile Believe)
#DanielAvery
https://danielavery.bandcamp.com/track/rapture-in-blue-w-cecile-believe-midnight-version
https://open.spotify.com/track/4VU2zt6DdkIQFGbLCLFIdX

🇺🇦 #NowPlaying on #BBC6Music's #RadcliffeAndMaconie
Daniel Avery:
🎵 Rapture in Blue (feat. Cecile Believe)
#DanielAvery
https://danielavery.bandcamp.com/track/rapture-in-blue-w-cecile-believe-midnight-version
https://open.spotify.com/track/4VU2zt6DdkIQFGbLCLFIdX