Tagged Questions

89 views

Is the domination number NP for non-bipartite graphs?

Calculating the domination number is an NP-Hard problem. Does it remain NP-Hard if we restrict it to non-bipartite graphs?
381 views

Seeming contradiction about P vs NP between graphclasses.org and at least two papers about clique in even-hole-free graphs

I believe correctness about clique in even-hole-free graphs of graphclasses.org and the paper Vertex elimination orderings for hereditary graph classes, Pierre Aboulker, Pierre Charbit, Nicolas ...
42 views

Cycles of Permutation Related to Rectangular Matrix Transposition

let the entries of a rectangular matrix $A\in\mathbb{C}^{m\times n}; m,n\in\mathbb{N}$ be stored in row-order in a linear vector $v$, i.e. $A_{i,j}=v_{i*m+j}$ Question: How can the first element ...
296 views

A combinatorial problem concerned with logic circuits

Consider a logic circuit with two-bit gates only. The length of each gate is the number of bit lines that the gate crosses. How hard is to compute the maximum length for a given circuit? Notice that ...
179 views

Making a graph claw-free by adding as few edges as possible

Independent set is polynomial in claw-free graphs, so I am wondering if this can approximate independent set. By adding enough edges to $G$ and gets claw-free $G'$. IS in $G'$ is IS in $G$, so this ...
163 views

Faster multiplication with a restricted set of multiplicands?

Let $A$ be a set of $k>1$ distinct elements from a semigroup. We wish to compute the product $$p=b_1 b_2 \cdots b_n$$ where each $b_i\in A$. Clearly $n-1$ multiplications suffice to compute $p$; ...
726 views

Examples of ubiquitous objects that are hard to find?

I've been wrestling with a certain research problem for a few years now, and I wonder if it's an instance of a more general problem with other important instances. I'll first describe a general ...
117 views

When is a power of an indeterminate in an ideal with 2 generators?

If I have an ideal ${\frak a} \colon= (f(X,S), g(X,S))$ of height $2$ in ${\Bbb C}[X, S]$, is it easy to know what power of $S$ is contained in $\frak a$? For example, what is the minimal number $m$? ...
104 views

Complexity of finding three perfect matchings with no edge in common in a bridgeless cubic graph

According to a conjecture: Conjecture (Fan & Raspaud, 1994) Every bridgeless cubic graph contains three perfect matchings with no edge in common. Equivalent statement here Main question: ...
125 views

Triangulations of a disk, flip distance and hamiltonian circuit

Let us consider a disk with one labelled point on the boundary and $n$ labelled points in the interior. Let T be a triangulation of the whole disk with vertices on the labelled points such that T ...
532 views

The smallest altitude amongst the triangles formed by points in the unit circle

Let $S$ be a finite set of points inside the unit circle. Consider all possible triangles formed by three distinct points in $S$, and among all such triangles find the smallest altitude. Denote this ...
62 views

maximum weight k-edge problem

Given positive integer $k$ and an undirected graph $(V,E)$, with nonnegative (non-uniform) weights on the nodes. Find $k$ edges whose spanning nodes have the maximum weight. Is this in P or NP? I ...
406 views

A simple language and systematic computations

The following somewhat popular simple computer language was enjoyed on sci.math, sci.math.research, pl.sci.matematyka, and perhaps before and after at several places (I wish I knew it's exact ...
35 views

Finite window transformations--input+output (pure algebra)

This q. presents a complete approach to my previous q.: Indecomposability of image transformations ... Let $\ A\ B\$ be finite sets of cardinality $\ > 1$.   Let $\ D:=A\times B$,   ...
142 views

NP-hardness of sparsest cut

Consider bipartitioning the vertices of a graph $(V,E)$ into $V = P \cup Q$ to minimize $$\frac{|E(P,Q)|}{|P| |Q|},$$ where $E(P,Q)$ denotes the set of edges in the cut. The usual citation for ...
87 views

Indecomposability of image transformations (pure algebra). Open questions

W-transformations -- definitions We will consider a class called finite window transformations $\ T:C^\mathbb Z\rightarrow C^\mathbb Z\$ defined a paragraph below; $\ \mathbb Z\$ is the ring of ...
716 views

How hard is reconstructing a permutation from its differences sequence?

My interest in combinatorially motivated computational problems led me to search for simple problems that turn out to be computationally hard. In this pursuit, I came up with a problem which I hope is ...
51 views

Is the $d$-dimensional Arrangement of Trees still $NP$-hard?

The $d$-dimensional Arrangement Problem for general graphs is known to be $NP$-hard since the special case $d=1$ (OLA) already is (Garey et al, [1976]). For Trees however, the one dimensional case can ...
288 views

Splay trees and Thompson's group $F$

( I apologize for only indicating some easy to find references, but new users are not allowed to link more than five). This is very speculative, but: Question: Is there a reformulation of the Dynamic ...
222 views

Maximal chain of 1s in binary strings

Let $S$ be the set of $2^n$ binary $n$-bit strings. For every $x\in S$, let $f(x)$ is the maximal chain of bits 1 in $x$. So Can we find a good upper bound of $$F(n)=\frac{\sum_{x\in S}f(x)}{2^n}$$ Of ...
230 views