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        All Questions

        1
        vote
        0answers
        34 views

        Succinct circuits and NEXPTIME-complete problems

        I am fascinated by a recent fact I was reading: Succinct Circuits are simple machines used to descibe graphs in exponentially less space, which leads to the downside that solving a problem on that ...
        3
        votes
        1answer
        117 views

        Representation of Subgraph Counts using Polynomial of Adjacency Matrix

        We consider a graph $G$ of size $d$ with adjacency matrix $A$, whose entries take value in $\{0,1\}$. We are interested in the number of a certain connected subgraph $S$ of size $k$ in $G$. For ...
        -4
        votes
        1answer
        195 views

        What is the computationally simplest way to universally index the set of simple graphs?

        If given a simple, integer-labeled, but not necessarily connected, graph $G := (V,E)$ consisting of at least one vertex, i.e. $\lvert \rvert V \lvert \rvert \geq 1$, then is there a function to ...
        1
        vote
        1answer
        58 views

        The complexity on calculation of the Graev metric on the free Boolean group of a metric space

        For a set $X$ by $B(X)$ we denote the family of all finite subsets of $X$ endowed with the operation $\oplus$ of symmetric difference. This operation turns $B(X)$ into a Boolean group, which can be ...
        2
        votes
        0answers
        29 views

        Flat or linkless embeddings of graph with fixed projection

        The problem of finding whether a given planar diagram of a graph, with over- and under-crossings, is a linkless embedding or not has unknown complexity (Kawarabayashi et al., 2010). My first question ...
        0
        votes
        1answer
        82 views

        Is there any solution that currently exists for the graph automorphism problem in the general case?

        I was reading the Wikipedia pages on the graph automorphism, but I could not find any solution to the problem (Not even a brute force one). So, is it indeed true that no solutions exist for the ...
        1
        vote
        0answers
        31 views

        Is there an algorithm for this constrained Hypergraph optimization problem?

        I'm currently developing an algorithm for computing knot coloring invariants and got to the following question: Given a set $S$ and a certain hyper-graph $H \subseteq S^3 $, find a decomposition $S = ...
        3
        votes
        0answers
        45 views

        Karp hardness of two cycles which lengths differ by one

        Our problem is as follows: NEARLY-EQUAL-CYCLE-PAIR Input: An undirected graph $G(V,E)$ Output: YES if there exists $2$ (simple) cycles in $G$ which lengths differ by $1$, otherwise NO Is ...
        6
        votes
        1answer
        107 views

        What is the complexity of counting Hamiltonian cycles of a graph?

        Since deciding whether a graph contains a Hamiltonian cycle is $NP$-complete, the counting problem which counts the number of such cycles of a graph is $NP$-hard. Is it also $PP$-hard in the sense ...
        6
        votes
        0answers
        104 views

        Does the problem of recognizing 3DORG-graphs have polynomial complexity?

        A 2DORG is the intersection graph of a finite family of rays directed $\to$ or $\uparrow$ in the plane. Such graphs can be recognized effectively (Felsner et al.). A 3DORG is the intersection graph of ...
        6
        votes
        0answers
        85 views

        Combinatorial region-halfplane incidence structures

        I've seen a bunch of similar MO questions, yet hopefully this is not a complete duplicate. Consider $n$ halfplanes in $\mathbb{R}^2$ with their borders in general position, that is, no point of $\...
        3
        votes
        0answers
        102 views

        $\mathrm{NP}$-complete problems in graph theory: undirected vs. directed

        Is it true that it is much easier to establish $\mathrm{NP}$-complete on undirected graphs than digraphs (directed graph)? Academic articles proving $\mathrm{NP}$-completeness of problems on ...
        4
        votes
        2answers
        95 views

        Is there an efficient way to represent all non-simple cycles of a digraph up to the number of vertices?

        Given two digraphs $G$ and $H$, I want a method for creating a bijection between all non-simple cycles of for all $n \le |V(G)|$. That means, given $C_G(n)$ and $C_H(n)$ being the sets of all non-...
        1
        vote
        0answers
        66 views

        Bipartite clustering is NP-hard?

        Let $G = (A\cup B, E)$ be a bipartite graph with edge weights $w: E\to \mathbb{R}$. Find a partition $B_1, B_2$ of $B$ and a nonempty disjoint subsets $A_1, A_2$ of $A$ such that $w(A_1,B_1) + w(A_2, ...
        16
        votes
        0answers
        263 views

        Straight-line drawing of regular polyhedra

        Find the minimum number of straight lines needed to cover a crossing-free straight-line drawing of the icosahedron $(13\dots 15)$ and of the dodecahedron $(9\dots 10)$ (in the plane). For example, ...

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        山西福彩快乐十分钟
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