<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>

Questions tagged [graph-theory]

Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

3,686 questions
Filter by
Sorted by
Tagged with
18 views

Can you create a directed graph on five vertices where each vertex touches every other vertex in one or two moves [on hold]

Can you create a directed graph on five vertices where each vertex touches every other vertex in one or two moves.
69 views

How does the complexity of calculating the Permanent imply the NP completeness of directed 3-cycle cover?

In their paper Two Approximation Algorithms for 3-Cycle Covers of Markus Bl?ser and Bodo Manthey it is stated that: "...deciding whether an unweighted directed graph has a 3-cycle cover is already NP-...
38 views

Coloration of an interval graph with constraints [on hold]

Given an interval graph that represents a set of tasks, in a given period of time, to be assigned to a set of employees, the objective is to find a minimum coloring of this graph such that the total ...
34 views

Algorithmic complexity of deciding the existence of regular $\mathrm{f}$-factors in graphs

Finding regular $\mathrm{f}$-factors in undirected simple graphs can be reduced to finding a perfect matching by utilizing the gadgets of Tutte or of Lovász and Plummer; there are several algorithms ...
141 views

Probability of a vertex being a “degree-celebrity” in a random graph

If $G(n,p)$ is a random graph of the Erd?s-Rényi model, what is the probability that $\mathrm{deg}(v)\gt\mathrm{deg}(u)\ \forall u\in\mathrm{adj}(v)$ Please feel free to relate answers to other ...
45 views

Polya Enumeration to study proper graph colorings

Can Polya enumeration technique or its modification be used in evaluating the chromatic polynomial of a simple graph? Specifically, we have to ensure that two distinct points have distinct colors if ...
76 views

Efficiently computable graph conductance measures

Treating electrical networks from a graph theory point of view, do there exist measures that characterize the overall electrical conductance of the graph whilst being efficiently computable? There ...
160 views

Thurston on the Robertson-Seymour theorem

Danny Calegari recounts here that Bill Thurston "gave one talk explaining his idea of a new proof of (some version of) the Robertson-Seymour theorem" at MSRI in 1996-1997. I could not find it in the ...
199 views

Reference for results about planar graphs

A colleague and I are writing a paper in which we need to make use of some basic facts about planar graphs. I would strongly prefer to simply give references for the results if possible, because the ...
122 views

Is this graph problem NP-Hard?

I had asked this question in math.se without any success Let $A$ be the symmetric $n\times n$ adjacency matrix for a graph where $A_{ij}$ is the positive edge value between node $i$ and $j$ (thus ...
160 views

Random walk on the hypercube with deleted edges

Let $G$ be the $n$-dimensional boolean hypercube, i.e. the graph on $\{0,1\}^n$ where two vertices are adjacent iff they differ on exactly one coordinate. Consider a graph $G'$ obtained by deleting a ...
713 views

When can a graph be oriented to form a Hasse diagram of a finite poset?

For any finite poset $P=(X,\leq)$ there is an undirected graph $G$ underlying the Hasse diagram of $P$ such that $V(G)=X$ and $E(G)=\{\{u,v\}:u\lessdot v\}$. With that said, is it possible to ...
92 views

Electrode assignment problem in resistive networks

Main question In the context of resistor networks, and particularly purely from a graph theory point of view, is there a consistent way of assigning the two electrode nodes in order to compare the ...
235 views
+50

Connected subgraphs and their sums

Let $G=(V,E)$ be an undirected graph with $|V|\geq 4$ such that for any distinct vertices $a_1,a_2,b_1,b_2$, there is a path from $a_1$ to $a_2$ and a (vertex-)disjoint path from $b_1$ to $b_2$. ...
119 views

Edge coloring graphs is in P?

It is known that there exist polynomial time algorithm to approximate the Lovasz number or the supremum of Shannon capacity of graphs. By Vizing's theorem, the graph $G$ has only two chromatic ...
58 views

Perfect graphs condition could be weakened?

The perfect graphs are generally defined as those graphs whose every induced subgraph has its chromatic number equal to its clique number. Now,are there some examples where the clique number of graph ...
81 views

Chromatic number of certain graphs with high maximum degree

Let $G$ be the graph of even order $n$ and size $\ge\frac{n^2}{4}$ which is a Cayley graph on a nilpotent group but not complete. Can the chromatic number of this graph be determined in polynomial ...
464 views

Is this representation of Go (game) irreducible?

This post is freely inspired by the basic rules of Go (game), usually played on a $19 \times 19$ grid graph. Consider the $\mathbb{Z}^2$ grid. We can assign to each vertex a state "black" ($b$), "...
66 views

81 views

Digraphs with same number of semiwalks

This is a follow-up question to Characterisation of walk-equivalent digraphs. Question: Do there exists two directed graphs $G$ and $H$ consisting of the same number ($n$) of vertices, such that \...
35 views

Generalization of Menger's Theorem to Infinite Graphs

Aharoni and Berger generalized Menger's Theorem to infinite graphs: For any digraph, and any subsets A and B, there is a family F of disjoint paths from A to B and a set separating B from A consisting ...
25 views

Worst case performance of heuristic for the non-eulerian Windy Postman Problem

The Windy Postman Problem seeks the cheapest tour in a complete undirected graph, that traverses each edge at least once; the cost of traversing an edge is positive and may depend on the direction, in ...
22 views

Definition of k-partite hypergraph

I would like to know the standard definition of k-partite hypergraph. There are two natural generalizations of k-partite graph to k-partite hypergraph: 1. For all edges e, any two vertices in e are ...
972 views

Examples of proofs by making reduction to a finite set [closed]

This is a very abstract question, I hope this is appropriate. Suppose $T$ is some claim over some infinite set $A$, for example, let $A$ be the set of all loopless planar graphs, and $T$ be the claim "...
88 views

60 views

Is there a well-posed definition of game on a graph? Or a well defined category of games on graphs?

All I ever found about this were natural language rules à la Asimov's three laws of robotics. The questions are straightforward questions: 1) Is there a well-posed mathematical definition of game on ...
29 views

Determining the minimum weight maximal oriented subgraph of a complete directed graph

Let $G(V,A,W):\ |V| = n,\ A=V\times V\setminus \lbrace (v,\ v)\rbrace,\ W\in\mathbb{R}_+^{n\times n},\ W^T\ne W$ be a complete directed graph with asymmetric weights. Questions: What is ...
58 views

Infimums of Poset of Unlabelled Subtrees

I will use $T$ to refer to the set of unlabelled, rooted trees, and use $(t,r)$ to denote a tree and its root. Let $(T, \preceq)$ be a poset where $(t_1,r_1) \preceq (t_2,r_2)$ means that $t_1$ is a ...
77 views

Two cospectral (normal) digraphs which are not orthogonal similar

Preliminaries A complex matrix $A$ is normal when $A$ and $A^*$ commute. A real matrix $A$ is normal when $A$ and $A^t$ commute. Two complex matrices $A$ and $B$ are said to be unitary similar if ...
230 views

Is there a name for this “stack” of graphs?

Let $G_1,\ldots,G_m$ be a sequence of graphs, all having the same number $n$ of vertices. For each pair $(G_i, G_{i+1})$ we add $n$ edges that connect the vertices of $G_i$ and $G_{i+1}$ bijectively. ...
132 views

Quotient graph of a tree

We know that every graph is isomorphic to a subgraph of a complete graph. Similarly, can we say that every graph is isomorphic to a quotient graph of a tree?
57 views

Combining three matchings to form a maximal matching

Consider a regular tripartite graph $G$ with maximum degree $\Delta\ge3$ and parts $A,B,C$. Now, the induced subgraphs $A\cup B, B\cup C$ and $A\cup C$ are all bipartite. Now, is there a way to ...
108 views

Bridged graphs sequence $g(n) =$ "Number of simple connected bridged graphs on $n+2$ nodes". We have $g(n)=1, 3, 10, 52, 351, 3714,\dots$ from A052446. Number formation sequence We also have $f(n) ... 1answer 67 views Minimizing the number of segments in drawings of planar graphs Every planar graph has at most$3n-6$edges, where$n\$ is the number of vertices. Moreover, every planar graph can be drawn with straight-line edges in the plane, without crossings. For example, for ...
128 views

Research-level blogs on complex networks:

I'm an applied mathematician that has a research interest in complex networks for modelling biological systems and I wondered whether the MathOverflow community might know of research-level blogs that ...

15 30 50 per page
山西福彩快乐十分钟

<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>