Is there a standard notation that expresses substructure? The specific case that I care about is the following: Suppose $\sigma,\tau$ are permutations such that $$\sigma(x)\not=x\ …

I'VE COMPLETELY REVISED MY QUESTION I wish to take a simple undirected graph (i.e. the complete graph K_4) Arbitrarily direct said graph, and then create a line graph from the d …

Hi there, I want to ask about the 2-cycle of K3 surface. As we know, its betti number $b_2$=22, so there will be 22 2-cycle generators. Is there any topological way to figure ou …

This might be a very naive question but here it goes. Let X be a smooth variety of dimension d over a p-adic field. We have the n part of the rerciprocity map: $rec/n: SK_1(X)/n \ …

Short version Is there an understanding of the emergence and subsequent disappearance of components with zero, one, or more cycles in a random subgraph of a square or cubic lattic …

A couple of questions related to edge-disjoint cycles. Let $K_n = (V,E)$ be the complete graph on $|V|=n$ nodes. Two cycles are 'edge disjoint' if they do not share any edges. …

Hey all, Not sure if this is a math problem or an algorithm problem - but hoping it has a math style answer. If I have a directed graph I can find all the closed loops - easy. ( …

I've posted a question on Stack Overflow regarding a seemingly NP-hard problem on maximization of weighted cycles in a graph problem. One of the respondents cited Professor David …

Consider the following definition. Let $C$ be a cycle of a simple graph $G$. We say that $C$ is convex if for any pair of distinct vertices $u,v \in V(C)$ $$ d_C(u,v) < d_{G-C} …

Can anyone give me a hint for an algorithm to find a simple cycle of length 4 (4 edges and 4 vertices that is) in an undirected graph, given as an adjacency list? It needs to use $ …

Let $S$ be the spectrum of $\mathbf{Z}$ or the spectrum of an algebraically closed field. (Actually, one can take $S$ to be any noetherian integral regular scheme.) Let $f:X\longr …

Hi guys, I have the following exercise to do but don't know how to approach it: Let G be a graph with n nodes (n ≥ 2), and where every node has degree at least 3. Show that G has …

Hi all, If anyone has insight into the following variant of the classic problem of packing vertex-disjoint cycle into graphs I would be interested. Given a finite undirected g …