All Questions
16 questions
8
votes
0
answers
152
views
Disjoint Rooted Paths with Specified Patterns
Let $S:=$ { $s_i : i \in [k]$ } and $T:=$ { $t_i : i \in [k]$ } be disjoint subsets of vertices of a graph $G$. Furthermore, let $A$ be a subset of $S_k$ (the symmetric group on $[k]$). A set of ...
- 32.1k
7
votes
2
answers
533
views
Recovering a Weighted Graph from Shortest Path Distances
I am interested in the following problem (A) and its related formulation (B).
(A) Suppose that $G = (V,E,w)$ is an unknown weighted graph on the vertex set $V$ and that one has access to $d_G(v,v'), \...
- 168
5
votes
1
answer
274
views
Is there a polynomial-time algorithm to check if a signed graph contains an odd-K5 minor?
I suspect this exists, if anyone has a reference please that would be very helpful.
By signed graph, I mean each edge is designated either odd or even (e.g. as in Guenin's result for weakly bipartite ...
- 311
5
votes
1
answer
183
views
Resource Constrained Routing with Refueling
What are good algorithms (resp. models) for calculating optimal or near optimal routes while taking into account fuel consumption, options for refueling and, limited tank capacity?
Especially modeling ...
- 13.2k
3
votes
1
answer
277
views
Theorems about the directed bandwidth of a rooted tree?
Let $T$ be a rooted tree with root $r$. Say an ordering $v_1,\ldots,v_n$ of the vertices of $T$ is a search order if $v_1=r$ and for all $2 \leq i \leq n$, there is $j < i$ such that $v_j$ is the ...
- 4,922
2
votes
3
answers
184
views
Reference Request for: Finding Large Bipartite Subgraphs via Destruction of Odd Cycles in Graphs
From the observation, that a bipartite graph doesn't contain odd cycles, it would seem natural to attempt to destroy all odd cycles in the most efficient way, by either removing edges or vertices of ...
- 13.2k
2
votes
0
answers
54
views
Do there (or might there) exist computable invariants for Aut(G)-invariant subgraphs of a graph G?
I am interested in algorithms for computing all subgraphs (not necessarily induced) of a graph $G$ up to $Aut(G)$ isomorphism. I had the idea of partitioning the edges of the graph like so
$$\{F|E(G)\...
- 161
2
votes
0
answers
106
views
Decomposing a planar graph
Thomassen proved that the vertex set of every planar graph can be decomposed into two sets inducing a 1-degenerate graph and a 2-degenerate graph, respectively (C. Thomassen, Decomposing a planar ...
- 3,153
2
votes
1
answer
68
views
finding dominating cycles in $2K_2$-free graphs
A cycle $C$ in a connected graph $G$ is called dominating if its complement $V(G)-V(C)$ is an independent set. H.J. Veldman proved in 1983 (Disc. Math. v.43, 281-96) a general result that in ...
- 14k
2
votes
0
answers
642
views
Hamiltonian paths in subgraphs of rectangular lattice graphs
Is following decision problem NP-hard / NP-complete:
Having vertex-induced subgraph of rectangular lattice graph determine if any Hamiltonian path exists
Having vertex-induced subgraph of rectangular ...
1
vote
2
answers
122
views
Maximal Minimum Weight DAGs
In the case of undirected, connected graphs the name for the maximal cycle-free subgraph of minimal weight is called Minimum Spanning Tree, and the efficient algorithms for their calculation are well ...
- 13.2k
1
vote
1
answer
311
views
Tutte's Reduction of Minimum Weight d-Factors to Matching
I am currently interested in minimum weight regular d-spanners (i.e. d-factors) of complete graphs. When searching the internet for related articles, I came across this one, which is concerned with ...
- 13.2k
1
vote
0
answers
52
views
Standard test for the recognition of toroidal graphs
Is there a standard test for the recognition of toroidal graphs? I have been using the Boyer–Myrvold planarity algorithm, which has a MATLAB and C++ implementation.
- 11
1
vote
1
answer
298
views
maximal sets of vertices that avoids a clique
I am looking for some known algorithm that finds, for a given graph, all the maximal sets of vertices that avoid a clique of some given size $k$. I'd prefer one written in MATLAB, but other languages ...
- 11
0
votes
0
answers
78
views
Sum of products on a directed acyclic graph
Is there a textbook/paper that I can reference for the following problem? I am looking for a concise proof that I can cite.
Let $G=(V,E)$ be a weighted directed acyclic graph, and consider
$s,t\in V$....
- 101
0
votes
0
answers
97
views
Shortest hyperpath algorithm in intuitionistic fuzzy hypergraphs
I was looking for an algorithm to calculate the shortest hyperpath in intuitionistic fuzzy hypergraphs and I found only this article (which propose two algorithms).
Are there any others algorithms ...
- 101