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Aequationes mathematicae, ISSN 0001-9054, 8/2019, Volume 93, Issue 4, pp. 735 - 742
We establish that for any connected graph G of order $$n \ge 6$$ n ≥ 6 , a minimum vertex-edge dominating set of G has at most n/3 vertices, thus affirmatively... 
Secondary 05C70 | Analysis | Mathematics | Vertex-edge domination | P_3$$ P 3 -packing | Combinatorics | Primary 05C69 | corona | extremal graph | packing | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | P-3-packing | Apexes | Graph theory
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 9/2019, Volume 35, Issue 5, pp. 1169 - 1177
A dominating set of a graph G is a set $$D\subseteq V_G$$ D ⊆ V G such that every vertex in $$V_G-D$$ V G - D is adjacent to at least one vertex in D, and the... 
05C76 | Domination number | Bipartization | Mathematics | Engineering Design | Bipartite graph | Combinatorics | 05C69 | 05C05 | MATHEMATICS | EQUAL DOMINATION | Graphs | Mathematics - Combinatorics
Journal Article
Opuscula Mathematica, ISSN 1232-9274, 2019, Volume 39, Issue 6, pp. 815 - 827
A set \(D\) of vertices of a graph \(G=(V_G,E_G)\) is a dominating set of \(G\) if every vertex in \(V_G-D\) is adjacent to at least one vertex in \(D\). The... 
certified domination | domination
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2019, Volume 265, pp. 142 - 157
In this paper, we study the concept of convex domination in maximal outerplanar graphs. For this class of graphs, we discuss several properties of this... 
Outerplanar | Convex guard set | Flipping edge | Convex domination | MATHEMATICS, APPLIED | NUMBERS | FLIP DISTANCE | TRIANGULATIONS | MONADIC 2ND-ORDER LOGIC | ALGORITHMS | Algorithms | Upper bounds | Graphs
Journal Article
Discrete Optimization, ISSN 1572-5286, 02/2020, Volume 35, p. 100553
A subset D⊆VG is a dominating set of G if every vertex in VG−D has a neighbor in D, while D is 2-dominating if every vertex in VG−D has at least two neighbors... 
Domination | NP-hardness | Certified domination | 2-domination | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | TREES | VERTICES
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 2018
Imagine that we are given a set D of officials and a set W of civils. For each civil x∈W, there must be an official v∈D that can serve  x, and whenever any... 
Domination | Nordhaus–Gaddum | Corona | Certified domination
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 08/2015, Volume 591, pp. 28 - 59
We consider the problem of searching for a mobile intruder hiding in a road network given as the union of two or more lines, or two or more line segments, in... 
Grids | Graph searching | Line segments | The searchlight problem | Lines | PLANE | COMPUTER SCIENCE, THEORY & METHODS | GUARDING PROBLEM | POLYGONAL REGION | PURSUIT-EVASION | OPTIMAL ALGORITHM | GRAPHS | Networks | Roads | Searchlights | Searching | Guards | Switching theory | Segments | Unions
Journal Article
GRAPHS AND COMBINATORICS, ISSN 0911-0119, 07/2017, Volume 33, Issue 4, pp. 991 - 998
In this note we present an alternative proof of the result by Dorfling et al. (Discrete Math 339(3):1180-1188, 2016) establishing that any maximal outerplanar... 
Domination | MATHEMATICS | Watched guards | Total domination | Outerplanar graph
Journal Article
Computational Geometry: Theory and Applications, ISSN 0925-7721, 05/2014, Volume 47, Issue 4, pp. 527 - 538
Given a set L of non-parallel lines in the plane, a watchman route (tour) for L is a closed curve contained in the union of the lines in L such that every line... 
NP-hardness | Watchman route | Dynamic programming | MATHEMATICS | MATHEMATICS, APPLIED | GRIDS | PLANE | ALGORITHM | SIMPLE POLYGONS | TIME | Computer science | Hardness | Algorithms | Tours | Computational geometry | Segments | Planes | Unions | Polygons
Journal Article
Journal of Computer and System Sciences, ISSN 0022-0000, 06/2019, Volume 102, pp. 57 - 68
Journal Article
Dissertationes Mathematicae, ISSN 0012-3862, 2008, Issue 450, pp. 5 - 132
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 12, pp. 4027 - 4036
We are interested in coloring the edges of a mixed graph, i.e., a graph containing unoriented and oriented edges. This problem is related to a communication... 
Trees | Mixed graphs | Edge coloring | Network communication | Precoloring extension | Bipartite graphs | Complexity | NP-COMPLETENESS | MATHEMATICS | Analysis | Algorithms
Journal Article
Computational Geometry: Theory and Applications, ISSN 0925-7721, 2007, Volume 37, Issue 2, pp. 59 - 71
A grid P is a connected union of vertical and horizontal segments. A mobile guard is a guard which is allowed to move along a grid segment, thus a point x is... 
Simple grids | Cooperative guards | Mobile guards | cooperative guards | MATHEMATICS | MATHEMATICS, APPLIED | mobile guards | simple grids | OPTIMAL ALGORITHM | GRAPHS | Algorithms
Journal Article
Information Processing Letters, ISSN 0020-0190, 2014, Volume 114, Issue 11, pp. 646 - 654
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 2019
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 03/2006, Volume 13, Issue 1 R, pp. 1 - 10
We prove that $\lfloor{n+h\over 4}\rfloor$ vertex guards are always sufficient to see the entire interior of an $n$-vertex orthogonal polygon $P$ with an... 
MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2010, Volume 24, Issue 3, pp. 1177 - 1204
We revisit the problem of pursuit-evasion in a grid introduced by Sugihara and Suzuki [SIAM J. Discrete Math., 2 (1989), pp. 126-143] in the line-of-sight... 
Grids | Pursuit-evasion game | Randomized algorithms | Line-of-sight vision model | COPS | MATHEMATICS, APPLIED | VISIBILITY | GAME | POLYGON | line-of-sight vision model | SEARCH | randomized algorithms | ROBBERS | pursuit-evasion game | grids | GRAPHS | Studies | Graphs | Game theory
Journal Article
Information Processing Letters, ISSN 0020-0190, 2008, Volume 106, Issue 4, pp. 133 - 135
In this note we observe that the problem of mixed graph coloring can be solved in linear time for trees, which improves the quadratic algorithm of Hansen et... 
Trees | Graph algorithms | Mixed graph coloring | GRAPH COLORINGS | COMPUTER SCIENCE, INFORMATION SYSTEMS | mixed graph coloring | trees | graph algorithms | Computer science | Analysis | Algorithms
Journal Article
Journal of Computer and System Sciences, ISSN 0022-0000, 06/2019, Volume 102, pp. 57 - 68
We study several problems of clearing subgraphs by mobile agents in digraphs. The agents can move only along directed walks of a digraph and, depending on the... 
NP-hardness | Monomial | Covering with paths | FPT-algorithm
Journal Article
Journal of Geometry, ISSN 0047-2468, 3/2006, Volume 84, Issue 1, pp. 164 - 185
The art gallery problem asks how many guards are sufficient to see every point of the interior of a polygon. A set of guards is called watched if each guard... 
Geometry | cooperative guards | art gallery problem | watched guards | Mathematics | 52C99 | Cooperative guards | Art gallery problem | Watched guards | Art dealers
Journal Article
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