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It's a good question for someone with a better memory than mine! There are two papers giving such constructions for regular multigraphs without loops. One is Ding and Chen, Generating r-regular grap …

Let $b\gt a\gt 0$ be constants. Define $P_n(a,b)$ to be the set of all $(x_1,\ldots,x_n)\in\mathbb{R}^n$ satisfying $$ |c_1 x_1 + \cdots + c_n x_n| \le 1$$ for every choice of $c_1,\ldots,c_n\in\lbra …

All graphs here are finite and simple. A $d$-factor of a graph is a spanning regular subgraph of degree $d$. Where can I find theorems of this nature, for constants $a,b,c\gt 0$: If $G$ is a graph w …

The following determinant arises in a combinatorial enumeration problem. I wonder if anyone has seen it before in any context or knows how to evaluate it. I tried computing it for small $n$ but didn't …

There are none. Write it in the monomial basis with respect to $x_1,\ldots,x_k$, with coefficients being polynomials in $y_1,\ldots,y_n$. The only monomial basis functions with $k$ variables such tha …

I think you will find it in Moon, J. W.; Moser, L. Almost all (0,1) matrices are primitive. Studia Sci. Math. Hungar. 1 (1966) 153–156. But I don't have time to visit the library to be sure and I don …

The paper of Schmidt that you found answers the question in the positive, both existence and algorithm. Start the DFS on $C$ and preferentially follow edges of $C$ until the final edge, which becomes …

bof got it right in a comment; here are the details. Let $T$ be a tournament with $n$ vertices. Label the vertices $v_1,\ldots,v_n$ in any way such that the $\binom n2$ values $|v_i-v_j|$ are distinct …

If disconnected cubic graphs are allowed, then probably user36212's answer is best possible for $n$ a multiple of 4. Is there a simple proof? If only connected cubic graphs are considered, Opstall an …

Almost all non-asymmetric graphs have exactly one non-trivial automorphism, namely a transposition swapping two vertices. So, an accurate estimate of their number is obtained by taking an arbitrary g …

There is some global parameter $n\to\infty$. And a function $N=N(n)\to\infty$. Let $X^n_1,X^n_2,\ldots,X^n_N$ be independent Bernoulli random variables, where $\delta\le P(X^n_i=1)=1-P(X^n_i=0)\le 1- …

If a sequence of 1-dimensional log-concave integer-valued distributions satisfies a Central Limit Theorem (CLT) and has variance going to $\infty$, then it satisfies a Local Central Limit Theorem (LCL …

The problem statement exactly corresponds to the definition of the hypergeometric distribution. With this key-phrase in hand, it is easy to locate an extensive literature. Start with wikipedia for ba …

It isn't hard to define a class of graphs whose isomorphism classes correspond to the isomorphism classes of loops. It is easiest using vertex colours: see B. D. McKay, A. Meynert and W. Myrvold, Sma …

I might be missing something, but it looks like you want a partition of the edges of $K_n$, odd $n$, into a set of subgraphs which are regular of degree 2. That's called a 2-factorization. It can be …