Results 1 to 10 of about 350 (134)
What do Eulerian and Hamiltonian cycles have to do with genome assembly? [PDF]
PLoS Computational Biology, 2021 Many students are taught about genome assembly using the dichotomy between the complexity of finding Eulerian and Hamiltonian cycles (easy versus hard, respectively).
Paul Medvedev, Mihai Pop
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MathematicsIn this paper, we explore the connection between sensor networks and graph theory. Sensor networks represent distributed systems of interconnected devices that collect and transmit data, while graph theory provides a robust framework for modeling and ...
Manuel Ceballos, María Millán
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Eulerian subgraphs containing given vertices and hamiltonian line graphs [PDF]
Discrete Mathematics, 1998 Let \(G\) be a graph and let \(D_1(G)\) be the set of vertices of degree 1 in \(G\). A graph is called an eulerian graph if it is connected and every vertex has even degree. An eulerian subgraph \(H\) of a graph \(G\) is called a dominating eulerian subgraph if \(G-V(H)\) is edgeless.
Hong-Jian Lai
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On Hamiltonian Decomposition Problem of 3-Arc Graphs. [PDF]
Comput Intell Neurosci, 2022 A 4‐tuple (y, x, v, w) in a graph is a 3‐arc if each of (y, x, v) and (x, v, w) is a path. The 3‐arc graph of H is the graph with vertex set all arcs of H and edge set containing all edges joining xy and vw whenever (y, x, v, w) is a 3‐arc of H. A Hamilton cycle is a closed path meeting each vertex of a graph.
Xu G, Sun Q, Liang Z.
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Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture. [PDF]
J Graph Theory, 2021 Abstract We study the existence of hamiltonian cycles in plane cubic graphs G having a facial 2‐factor Q. Thus hamiltonicity in G is transformed into the existence of a (quasi) spanning tree of faces in the contraction G ∕ Q. In particular, we study the case where G is the leapfrog extension (called vertex envelope of a plane cubic graph G 0.
Bagheri Gh B +3 more
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Hamiltonian problems in edge-colored complete graphs and eulerian cycles in edge-colored graphs : some complexity results [PDF]
RAIRO - Operations Research, 1996 Summary: In an edge-colored graph, we say that a path (cycle) is alternating if it has length at least 2 (3) and if any 2 adjacent edges of this path (cycle) have different colors. We give efficient algorithms for finding alternating factors with a minimum number of cycles and then, by using this result, we obtain polynomial algorithms for finding ...
Y Manoussakis
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SOME PROPERTIES ON COPRIME GRAPH OF GENERALIZED QUATERNION GROUPS
Barekeng, 2023 A coprime graph is a representation of finite groups on graphs by defining the vertex graph as an element in a group and two vertices adjacent to each other's if and only if the order of the two elements is coprime.
Arif Munandar
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Notes on upper bounds for the largest eigenvalue based on edge-decompositions of a signed graph
Kuwait Journal of Science, 2023 The adjacency matrix of a signed graph has +1 or -1 for adjacent vertices, depending on the sign of the connecting edge. According to this concept, an ordinary graph can be interpreted as a signed graph without negative edges.
Zoran Stanić
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Mathematics, 2023 Fuzzy Topological Topographic Mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem.
Noorsufia Abd Shukor +4 more
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Spanning eulerian subdigraphs in semicomplete digraphs
Journal of Graph Theory, Volume 102, Issue 3, Page 578-606, March 2023., 2023 Abstract A digraph is eulerian if it is connected and every vertex has its in‐degree equal to its out‐degree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first characterize the pairs (D,a) $(D,a)$ of a semicomplete digraph D $D$ and an arc a $a$ such that D $D$ has a spanning eulerian ...
Jørgen Bang‐Jensen +2 more
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