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\begin{document}
\title{On the Representability of Line Graphs}
\begin{abstract}
A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)$ is in $E$ for each $x$ not equal to $y$. The motivation to study representable gra... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum value of \( n \) such that the line graph \( L(W_n) \) of the wheel graph \( W_n \) is guaranteed to be non-representable? Additionally, provide an example of a graph \( G \) for which \( L^k(G) \) is non-representable for \( k \geq 4 \). | 91,196 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{On second-order differentiability with respect to parameters for differential equations with state-dependent delays\thanks{This research was partially supported by the Hungarian National Foundation for Scientific Research Grant No. K73274.}} \author{Ferenc Hartung\\ Department of Mathematics\\... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a class of differential equations with state-dependent delays of the form
\[
\dot{x}(t) = f(t, x_t, x(t - \tau(t, x_t, \xi)), \theta), \quad t \in [0, T],
\]
where \( f \) is Lipschitz continuous in its arguments, and let \(\tau\) be a piecewise strictly monotone delay function, determine the necessary and su... | 59,364 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{\bf Quantum speed limit time for a two-qubit system interacting with independent and common reservoirs } \author{ N. Behzadi $^{a}$ \thanks{E-mail:n.behzadi@tabrizu.ac.ir} , A. Ektesabi $^{b}$ , B. Ahansaz $^{b}$, E. Faizi $^{b}$ \\ $^a${\small Research Institute for Fundamental Sciences, Uni... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the relationship between the quantum speed limit time \( \tau_{QSL} \) and the coupling strength \( \gamma_{0} \) for a two-qubit system initially prepared in extended Werner-like states when interacting with a common reservoir compared to independent reservoirs, specifically in the context of entering the non-... | 58,699 | mlfoundations-dev/gair_mathpile | |
"\\begin{document}\n\n\\title{Producing delocalized frequency-time Schr\\\"odinger cat-like states w(...TRUNCATED) | arXiv | arXiv/math_arXiv_v0.2.jsonl | "What is the maximum number of oscillations observed in the coincidence probability in a Hong-Ou-Man(...TRUNCATED) | 27,739 | mlfoundations-dev/gair_mathpile | |
"\\begin{document}\n\n\\title{On the slope of fourgonal semistable fibrations}\n\n\\markboth{Beorchi(...TRUNCATED) | arXiv | arXiv/math_arXiv_v0.2.jsonl | "Given a semistable fibration \\( f: S \\to B \\), where the general fiber is a smooth fourgonal cur(...TRUNCATED) | 74,186 | mlfoundations-dev/gair_mathpile | |
"\\begin{document}\n\n\\title[]{Generalized Bernstein operators on the classical polynomial spaces}\(...TRUNCATED) | arXiv | arXiv/math_arXiv_v0.2.jsonl | "Let \\( f_1(x) \\) be a polynomial of degree \\( m \\geq 1 \\) that is strictly increasing on the i(...TRUNCATED) | 3,035 | mlfoundations-dev/gair_mathpile | |
"\\begin{document}\n\n\\title{On 4-reflective complex analytic planar billiards} \\begin{abstract} T(...TRUNCATED) | arXiv | arXiv/math_arXiv_v0.2.jsonl | "What are the necessary and sufficient conditions for a collection of four holomorphic curves in the(...TRUNCATED) | 14,594 | mlfoundations-dev/gair_mathpile | |
"\\begin{document}\n\n\\begin{abstract} Place one active particle at the root of a graph and a Poiss(...TRUNCATED) | arXiv | arXiv/math_arXiv_v0.2.jsonl | "In the context of the threshold frog model on an infinite complete $d$-ary tree, if the number of i(...TRUNCATED) | 74,756 | mlfoundations-dev/gair_mathpile | |
"\\begin{document}\n\n\\title{Deletion-Contraction and the Surface Tutte Polynomial}\n\n\\begin{abst(...TRUNCATED) | arXiv | arXiv/math_arXiv_v0.2.jsonl | "Let \\( G \\) be a connected, orientable ribbon graph with \\( v \\) vertices, \\( e \\) edges, and(...TRUNCATED) | 89,786 | mlfoundations-dev/gair_mathpile | |
"\\begin{document}\n\n\\author{K\\k{e}stutis \\v{C}esnavi\\v{c}ius} \\title{\\resizebox{\\textwidth}(...TRUNCATED) | arXiv | arXiv/math_arXiv_v0.2.jsonl | "What is the relationship between the $\\ell$-parity conjecture and the root numbers of abelian vari(...TRUNCATED) | 48,636 | mlfoundations-dev/gair_mathpile |
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