## LaTeX and evince problem. Evince does not attach to edges of the screen

I just use ST3 for LaTeX. LaTeXTools requires one of this pdf-viewers: evince, okular, zathura. I like evince because it is very simple and fast pdf-viewer. But have an issue: when I compile my pdf file and then evince open it, it just does not attach to left or right edges of the screen. I still can attach it to top or bottom edges, but it is do not convenient to use.

Even I close the file and open singly from ST3, issue still is. If I open an another file which was not build with LaTeXTools, there is not the issue.

## Savage Worlds (SWADE) – Implication of permanent injuries (specifically reducing an attribute by a die type) on Edges and weapon use?

If a character in Savage Worlds gains an injury that permanently reduces the die type for an attribute, does that mean that all Edges that were dependant on that attribute are no longer valid? If so, what does that mean for the character? Do they get to replace the Edges with something else or do they just lose it forever?

e.g. A character has a d8 in Agility and buys the Extraction Edge during char. creation, which has a prerequisite Agility of d8+. During combat, they’re incapacitated, fail the Vigor roll, and roll “Broken” on the Injury Table (Agility reduced a die type).
What happens to their Extraction Edge?

Does the same rule apply for what kind of weapon they can use? Let’s say they usually use a weapon that has a min. strength of d8, but the character’s strength is now a d6 – can they no longer use that weapon? Does this happen while the attribute is temporarily reduced, too (as in, they get a temporary injury instead of a permanent one)? The answer to this question might seem obvious, but the reason I ask is because the character in question has the Trademark Weapon Edge, and the weapon has a min. str. of d8. If they can no longer wield that weapon, does that Edge become useless?

## Finding partition with maximum number of edges between sets

Given a graph (say in adjacency list form), is there an algorithm to find a partition of vertices such that the number of edges between the two sets of the partition is the maximum possible?

For example, for the following set of edges of a graph with vertex set $$\{1, 2, 3, 4, 5, 6\}$$: $$\{(1, 2), (2, 3), (3, 1), (4, 5) , (5, 6), (6, 4)\}$$, one possible “maximum” partition is $$\{\{1, 3, 4, 6\}, \{2, 5\}\}$$ with $$4$$ edges between the sets $$\{1, 3, 4, 6\}$$ and $$\{2, 5\}$$.

## Forward edges in undirected grapth using BFS

Introduction to Algorithms books claims BFS only classifies an edge for an undirected graph to be either tree or cross edge. But how about this simple example below where forward edges are naturally appearing?

Given graph with just 2 vertices A and B and 3 edges from A to B!

(1) A->B (tree edge, A is now marked as an ancestor for B and B is A’s descendant)

(2) A->B (forward edge? B is not yet processed (gray) and we found an edge to it from its ancestor(A))

(3) A->B forward edge using the same reasoning as in (2)!

What am I missing here?

## Like transitive reduction, but removing vertices rather than edges?

Suppose I have a directed graph $$G = (V, E)$$ (or, which is the same, a relation on the set $$V$$ as defined by the adjacency matrix) that may contain three vertices $$x, y, z$$ such that $$xy, xz, yz \in E$$ — that is to say, the relation restricted to $$x, y, z$$ is transitive, there is a triangle. Let us call this situation a “local transitivity”. My goal is to obtain all the subgraphs of $$G$$ induced by cutting middle vertices from local transitivities until none remain, which I dub “resolution”.

There may be multiple solutions. For instance, consider a graph given by this relation:

  a b c d   a □ ■ ■ □   b □ □ ■ ■   c □ □ □ ■   d □ □ □ □   

(It looks like a square with one diagonal.)

There are two ways it can be resolved:

  a b d        a c d   a □ ■ □      a □ ■ □   b □ □ ■      c □ □ ■   d □ □ □      d □ □ □   

One way I can compute the resolutions of a graph is by giving a “non-deterministic” function $$f :G \rightarrow \{G\}$$ that removes any single local transitivity. Repeatedly applying $$f$$ to any graph, I will eventually converge to a set of induced subgraphs completely devoid of local transitivities.

One way to define $$f$$ is by considering all the triples of distinct vertices and checking them for local transitivity. From each matching triple, the middle vertex is extracted, and any of these vertices is cut. But there is about $$|V|^3$$ such triples.

Is there a better way? Is there prior art that I may study?

## Directed Trees: Finding all the edges and vertices in a specific direction

I am an electrical engineer without experience in graph theory. However, I have a problem which I believe can be solved by graph theory. We have a directed tree, such as the one below. We want to find all the vertices and edges starting from a vertex in a given direction. For instance, in the figure below, we want to identify the vertices and edges downward from vertex 1 (the red lines). Is there an algorithm to do this (preferably in MATLAB)? The edges have equal weight.

## Looking for a similar graph algorithm to generate a graph given the edges a path took

I’m looking for some help on algorithms that may help generate a directed non-cyclic graph from a list of leaf nodes and the incomplete set of edge nodes taken to get to the leaf node.

For example, let’s say we have a node that has multiple edges to other nodes and we label the two edges from Node A “a:1”, “a:2”. At the end, we have a few leaf nodes and we’ve recorded the paths to get there as [“a:1”, “b:2”],[“a:2″,”c:1”]. Which would mean you can get there by the first edge of A and 2nd edge of B, or the 2nd edge of A and the first edge of C.

If we only describe the edge nodes, and either their full or partial unordered paths, what are some methods to generate trees that include those paths?

ex:

leaf1 = ["a:1", "b:1"],["a:2","c:1"] leaf2 = ["a:2", "c:2"] leaf3 = ["c:3"] 

May generate something like:

or a little more cleanly,

What’s not important is unique edges, but rather if you’re ‘collecting information’ each time you pass through a node, that by the time you reach a leaf node you’ve you’ve collected the required information for all the leaf nodes. This may mean a single edge points to multiple leaf nodes as in the first example.

It seems like you would start by determining which options are subsets of one another, and then recursively start adding in the nodes which would lead to the most leaf nodes. The nodes with the most specific path would likely be the last nodes created. Or potentially creating the trees for each leaf node and then merging them together.

I couldn’t find an algorithm for this kind of generation, so even a starting point would help.

## Min cut of at most k edges

I have been studying for my algorithms exam and whilst doing previous exams found this question for which I am not sure how to handle. Given a Graph with integer capacities, find an efficient algorithm to determine whether the graph has a min cut of at most k edges (in the question k = 100) or not.

My thinking was computing a min cut, then for every edge on that cut, increase it by 1 and compute the min cut again – if the max flow has risen, that means that that edge exists in every single min cut. And If I found there to be over 100 of these edges, then there is no min cut of at most k edges.

However, I don’t think that if I found there to be less 100 of these edges, there’s necessarily a min cut of at most 100 edges.

Anyone care to give a helping hand? Thank you!

## how to maximise the no of edges selected in the graph in form of cycles of unbounded length?

Recently i started looking the perfect cycle cover algorithm related to kidney exchange problem where it is considered as NP-Complete for cycles restricted to a length>2. However if cycles are not restricted by removing the length constraint it is considered as solvable in polynomial time ,But if perfect cycle cover doesn’t exist and just we need to maximise the no of edges selected in form of cycles(So as to maximise the no of kidney exchanges), also no restriction on cycle’s length, then how do we do it?

I am thinking of finding all cycles in the graph and then one by one remove the cycle’s edges from the graph and then find the cycles in the residual graph and so on till no more cycles exist and then sum up all the cycle’s lengths continuing this for all cycles and find the solution with maximum edges selected. But since this is not a good solution i want to know how to solve this maximising problem