Ben Seamone

Ben Seamone
Université de Montréal | UdeM · Department of Computer Science and Operations Research

PhD

About

28
Publications
2,187
Reads
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234
Citations
Citations since 2017
15 Research Items
127 Citations
20172018201920202021202220230510152025
20172018201920202021202220230510152025
20172018201920202021202220230510152025
20172018201920202021202220230510152025
Introduction
Graph structure; graph searching & surveillance
Additional affiliations
April 2015 - present
Université de Montréal
Position
  • Professor
September 2012 - August 2014
Université de Montréal
Position
  • PostDoc Position
June 2005 - present
Dawson College
Position
  • Professor
Education
September 2008 - August 2012
Carleton University
Field of study
  • Applied Mathematics
September 2003 - December 2004
University of Waterloo
Field of study
  • Combinatorics and Optimization
September 1999 - April 2003
Mount Allison University
Field of study
  • Mathematics (honours)

Publications

Publications (28)
Preprint
Full-text available
This paper studies two variants of defective acyclic coloring of planar graphs. For a graph $G$ and a coloring $\varphi$ of $G$, a 2CC transversal is a subset $E'$ of $E(G)$ that intersects every 2-colored cycle. Let $k$ be a positive integer. We denote by $m_k(G)$ the minimum integer $m$ such that $G$ has a proper $k$-coloring which has a 2CC tran...
Preprint
We fully disprove a conjecture of Haythorpe on the minimum number of hamiltonian cycles in regular hamiltonian graphs, thereby extending a result of Zamfirescu, as well as correct and complement Haythorpe's computational enumerative results from [Experim. Math. 27 (2018) 426-430]. Thereafter, we use the Lov\'asz Local Lemma to extend Thomassen's in...
Article
Full-text available
Recently, a conjecture due to Hendry was disproved which stated that every Hamiltonian chordal graph is cycle extendible. Here we further explore the conjecture, showing that it fails to hold even when a number of extra conditions are imposed. In particular, we show that Hendry's Conjecture fails for strongly chordal graphs, graphs with high connec...
Article
The edge clique cover number ecc ( G ) of a graph G is the size of the smallest collection of complete subgraphs whose union covers all edges of G . Chen, Jacobson, Kézdy, Lehel, Scheinerman, and Wang conjectured in 2000 that if G is claw‐free, then ecc ( G ) is bounded above by its order (denoted n ). Recently, Javadi and Hajebi verified this conj...
Article
We show that there is a constant C such that for any b < n/ln n − Cn/(ln n)3/2, Maker can win the Maker-Breaker Hamilton cycle game in n + Cn/√ln n steps.
Article
We show Maker wins the Maker-Breaker perfect matching game in n/2 + o(n) turns when the bias is at least n/ln n − f(n)n/(ln n)5/4, for any f going to infinity with n and n sufficiently large (in terms of f).
Preprint
Full-text available
We show that Maker wins the Maker-Breaker perfect matching game in $\frac{n}{2}+o(n)$ turns when the bias is at least $\frac{n}{\log{n}}-\frac{f(n)n}{(\log{n})^{5/4}}$, for any $f$ going to infinity with $n$ and $n$ sufficiently large (in terms of $f$).
Preprint
Full-text available
We show that there is a constant C such that for any $b<\frac{n}{\ln{n}}-\frac{Cn}{(\ln{n})^{3/2}}$, Maker wins the Maker-Breaker Hamilton cycle game in $n+\frac{Cn}{\sqrt{\ln{n}}}$ steps.
Preprint
Recently, a conjecture due to Hendry was disproved which stated that every Hamiltonian chordal graph is cycle extendible. Here we further explore the conjecture, showing that it fails to hold even when a number of extra conditions are imposed. In particular, we show that Hendry's Conjecture fails for strongly chordal graphs, graphs with high connec...
Preprint
Full-text available
In the eternal domination game, an attacker attacks a vertex at each turn and a team of guards must move a guard to the attacked vertex to defend it. The guards may only move to adjacent vertices and no more than one guard may occupy a vertex. The goal is to determine the eternal domination number of a graph which is the minimum number of guards re...
Article
An eternal dominating set of a graph G is a set of vertices (or “guards”) which dominates G and which can defend any infinite series of vertex attacks, where an attack is defended by moving one guard along an edge from its current position to the attacked vertex. The size of the smallest eternal dominating set is denoted γ∞(G) and is called the ete...
Preprint
Full-text available
An eternal dominating set of a graph $G$ is a set of vertices (or "guards") which dominates $G$ and which can defend any infinite series of vertex attacks, where an attack is defended by moving one guard along an edge from its current position to the attacked vertex. The size of the smallest eternal dominating set is denoted $\gamma^\infty(G)$ and...
Preprint
Full-text available
We consider the well-studied cops and robbers game in the context of oriented graphs, which has received surprisingly little attention to date. We examine the relationship between the cop numbers of an oriented graph and its underlying undirected graph, giving a surprising result that there exists at least one graph $G$ for which every strongly con...
Preprint
Full-text available
We study a variation of the classical pursuit-evasion game of Cops and Robbers in which agents are required to move to an adjacent vertex on every turn. We explore how the minimum number of cops needed to catch the robber can change when this condition is added to the rules of the game. We study this `Fully Active Cops and Robbers' game for a numbe...
Article
Full-text available
A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian. We also show that this is best possible by exhibiting uniquely Hamiltonian claw-free graphs with minimum degree 2 and arbitrary maximum degree. Finally, we show that...
Article
Graph Theory International audience Let G = (V,E) be a graph. For each e ∈E(G) and v ∈V(G), let Le and Lv, respectively, be a list of real numbers. Let w be a function on V(G) ∪E(G) such that w(e) ∈Le for each e ∈E(G) and w(v) ∈Lv for each v ∈V(G), and let cw be the vertex colouring obtained by cw(v) = w(v) + ∑ₑ ∋vw(e). A graph is (k,l)-weight choo...
Article
Full-text available
In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater. We disprove this conjecture by constructing counterexamples on $n$ vertices for any $n \geq 15$. Furthermore, we show that there exist counterexamples where the rati...
Article
Full-text available
The 1-2-3 Conjecture, posed in 2004 by Karonski, Luczak, and Thomason, is as follows: "If G is a graph with no connected component having exactly 2 vertices, then the edges of G may be assigned weights from the set {1,2,3} so that, for any adjacent vertices u and v, the sum of weights of edges incident to u differs from the sum of weights of edges...
Article
Karonski, Luczak, and Thomason (2004) conjectured that, for any connected graph G on at least three vertices, there exists an edge weighting from {1,2,3} such that adjacent vertices receive different sums of incident edge weights. Bartnicki, Grytczuk, and Niwcyk (2009) made a stronger conjecture, that each edge's weight may be chosen from an arbitr...
Article
Full-text available
In 2004, Karonski, Luczak, and Thomason conjectured that the edges of any connected graph on at least 3 vertices may be weighted from the set {1,2,3} so that the vertices are properly coloured by the sums of their incident edge weights. A subsequent conjecture by Przybylo and Wozniak (2010) states that weights from {1,2} suffice if one also weights...
Article
If G is a finite group of order n, we denote by KG the complete Cayley graph on G. Let L be a multiset of group elements of G. If KG contains a subgraph whose edge labels are precisely L then we say that L is realizable as a G-subgraph. For an arbitrary finite group G, we present necessary and sufficient conditions for a multiset L to be realizable...
Article
Full-text available
Graphs and Algorithms International audience An edge-weighting vertex colouring of a graph is an edge-weight assignment such that the accumulated weights at the vertices yields a proper vertex colouring. If such an assignment from a set S exists, we say the graph is S-weight colourable. It is conjectured that every graph with no isolated edge is \1...
Article
Full-text available
An edge-weighting vertex colouring of a graph is an edge-weight assignment such that the accumulated weights at the vertices yield a proper vertex colouring. If such an assignment from a set S exists, we say the graph is S-weight colourable. We consider the S-weight colourability of digraphs by defining the accumulated weight at a vertex to be the...
Conference Paper
Full-text available
We show that the Yao graph Y 4 in the L 2 metric is a spanner with stretch factor 8Ö2(29+23Ö2)8\sqrt{2}(29+23\sqrt{2}).
Article
Full-text available
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor 8(29+23sqrt(2)). Enroute to this, we also show that the Yao graph Y4 in the Linf metric is a planar spanner with stretch factor 8.
Article
Abstract A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen. Key words: C-independent set, Lov¶asz Local Lemma, Uniquely hamiltonian

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Projects (5)
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Papers which don't fit elsewhere