Anders Yeo
YOU?
Author Swipe
View article: Generalized paths and cycles in semicomplete multipartite digraphs
Generalized paths and cycles in semicomplete multipartite digraphs Open
A digraph is semicomplete if it has no pair of non-adjacent vertices. It is complete if every pair of distinct vertices induces a 2-cycle. A digraph is semicomplete multipartite if it can be obtained from a semicomplete digraph D by choosi…
View article: Judicious Partitions in Edge-Weighted Graphs with Bounded Maximum Weighted Degree
Judicious Partitions in Edge-Weighted Graphs with Bounded Maximum Weighted Degree Open
In this paper, we investigate bounds for the following judicious $k$-partitioning problem: Given an edge-weighted graph $G$, find a $k$-partition $(V_1,V_2,\dots ,V_k)$ of $V(G)$ such that the total weight of edges in the heaviest induced …
View article: Extensions and applications of the Tuza-Vestergaard theorem
Extensions and applications of the Tuza-Vestergaard theorem Open
The transversal number τ(H) of a hypergraph H is the minimum number of vertices that intersect every edge of H. A 6-uniform hypergraph has all edges of size 6. On 10 November 2000 Tuza and Vestergaard (2002) conjectured that if H is a 3-re…
View article: Note on the size of a stable matching
Note on the size of a stable matching Open
Consider a one-to-one two-sided matching market with workers on one side and single-position firms on the other, and suppose that the largest individually rational matching contains $n$ pairs. We show that the number of workers employed an…
View article: Number of Subgraphs and Their Converses in Tournaments and New Digraph Polynomials
Number of Subgraphs and Their Converses in Tournaments and New Digraph Polynomials Open
An oriented graph is converse invariant if, for any tournament , the number of copies of in is equal to that of its converse . El Sahili and Ghazo Hanna [J. Graph Theory 102 (2023), 684‐701] showed that any oriented graph with maximum degr…
View article: Oriented discrepancy of Hamilton cycles and paths in digraphs
Oriented discrepancy of Hamilton cycles and paths in digraphs Open
Erd{\H o}s (1963) initiated extensive graph discrepancy research on 2-edge-colored graphs. Gishboliner, Krivelevich, and Michaeli (2023) launched similar research on oriented graphs. They conjectured the following generalization of Dirac's…
View article: Finding all stable matchings with assignment constraints
Finding all stable matchings with assignment constraints Open
In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main con…
View article: Upper bounds on minimum size of feedback arc set of directed multigraphs with bounded degree
Upper bounds on minimum size of feedback arc set of directed multigraphs with bounded degree Open
An oriented multigraph is a directed multigraph without directed 2-cycles. Let ${\rm fas}(D)$ denote the minimum size of a feedback arc set in an oriented multigraph $D$. The degree of a vertex is the sum of its out- and in-degrees. In sev…
View article: Speeding up deferred acceptance
Speeding up deferred acceptance Open
A run of the deferred acceptance (DA) algorithm may contain proposals that are sure to be rejected. We introduce the accelerated deferred acceptance algorithm that proceeds in a similar manner to DA but with sure-to-be rejected proposals r…
View article: Generalized paths and cycles in semicomplete multipartite digraphs
Generalized paths and cycles in semicomplete multipartite digraphs Open
It is well-known and easy to show that even the following version of the directed travelling salesman problem is NP-complete: Given a strongly connected complete digraph $D=(V,A)$, a cost function $w: A\rightarrow \{0,1\}$ and a natural nu…
View article: Lower Bounds for Maximum Weight Bisections of Graphs with Bounded Degrees
Lower Bounds for Maximum Weight Bisections of Graphs with Bounded Degrees Open
A bisection in a graph is a cut in which the number of vertices in the two parts differ by at most 1. In this paper, we give lower bounds for the maximum weight of bisections of edge-weighted graphs with bounded maximum degree. Our results…
View article: Note on Disjoint Cycles in Multipartite Tournaments
Note on Disjoint Cycles in Multipartite Tournaments Open
In 1981, Bermond and Thomassen conjectured that for any positive integer $k$, every digraph with minimum out-degree at least $2k-1$ admits $k$ vertex-disjoint directed cycles. In this short paper, we verify the Bermond-Thomassen conjecture…
View article: Some coordination problems are harder than others
Some coordination problems are harder than others Open
In order to coordinate players in a game must first identify a target pattern of behaviour. In this paper we investigate the difficulty of identifying prominent outcomes in two kinds of binary action coordination problems in social network…
View article: Transversals in regular uniform hypergraphs
Transversals in regular uniform hypergraphs Open
The transversal number of a hypergraph is the minimum number of vertices that intersect every edge of . This notion of transversal is fundamental in hypergraph theory and has been studied a great deal in the literature. A hypergraph is ‐re…
View article: On Seymour's and Sullivan's second neighbourhood conjectures
On Seymour's and Sullivan's second neighbourhood conjectures Open
For a vertex of a digraph, (, respectively) is the number of vertices at distance 1 from (to, respectively) and is the number of vertices at distance 2 from . In 1995, Seymour conjectured that for any oriented graph there exists a vertex s…
View article: Subeulerian Oriented Graphs
Subeulerian Oriented Graphs Open
A graph is subeulerian if it is a spanning subgraph of an eulerian graph. All subeulerian graphs were characterized by Boesch, Suffel, Tindell in 1977. Later, a simple proof of their theorem was given by Jaeger. A digraph D is eulerian if …
View article: Complexity of Efficient Outcomes in Binary-Action Polymatrix Games and Implications for Coordination Problems
Complexity of Efficient Outcomes in Binary-Action Polymatrix Games and Implications for Coordination Problems Open
We investigate the difficulty of finding economically efficient solutions to coordination problems on graphs. Our work focuses on two forms of coordination problem: pure-coordination games and anti-coordination games. We consider three obj…
View article: (1,1)-Cluster Editing is polynomial-time solvable
(1,1)-Cluster Editing is polynomial-time solvable Open
A graph H is a clique graph if H is a vertex-disjoin union of cliques. Abu-Khzam (2017) introduced the (a,d)-Cluster Editing problem, where for fixed natural numbers a,d, given a graph G and vertex-weights a∗:V(G)→{0,1,…,a} and d∗:V(G)→{0,…
View article: Complexity Dichotomies for the Maximum Weighted Digraph Partition Problem
Complexity Dichotomies for the Maximum Weighted Digraph Partition Problem Open
We introduce and study a new optimization problem on digraphs, termed Maximum Weighted Digraph Partition (MWDP) problem. We prove three complexity dichotomies for MWDP: on arbitrary digraphs, on oriented digraphs, and on symmetric digraphs…
View article: On Seymour's and Sullivan's Second Neighbourhood Conjectures
On Seymour's and Sullivan's Second Neighbourhood Conjectures Open
For a vertex $x$ of a digraph, $d^+(x)$ ($d^-(x)$, resp.) is the number of vertices at distance 1 from (to, resp.) $x$ and $d^{++}(x)$ is the number of vertices at distance 2 from $x$. In 1995, Seymour conjectured that for any oriented gra…
View article: Complexity of Efficient Outcomes in Binary-Action Polymatrix Games with Implications for Coordination Problems
Complexity of Efficient Outcomes in Binary-Action Polymatrix Games with Implications for Coordination Problems Open
We investigate the difficulty of finding economically efficient solutions to coordination problems on graphs. Our work focuses on two forms of coordination problem: pure-coordination games and anti-coordination games. We consider three obj…
View article: Bounds on Maximum Weight Directed Cut
Bounds on Maximum Weight Directed Cut Open
We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum …
View article: Results on the small quasi-kernel conjecture
Results on the small quasi-kernel conjecture Open
A quasi-kernel of a digraph D is an independent set Q⊆V(D) such that for every vertex v∈V(D)﹨Q, there exists a directed path with one or two arcs from v to a vertex u∈Q. In 1974, Chvátal and Lovász proved that every digraph has a quasi-ker…
View article: Exact capacitated domination: On the computational complexity of uniqueness
Exact capacitated domination: On the computational complexity of uniqueness Open
Gerke et al. (2019) introduced a game-theoretic model to study public good provision in social networks when there are constraints on sharing. This model generates a purely graph-theoretic problem termed exact capacitated domination. In th…