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Chordal graphs: Cycles of length 4 or more Induced subgraph [6] Perfect graphs: Cycles of odd length 5 or more or their complements: Induced subgraph [7] Line graph of graphs: 9 forbidden subgraphs: Induced subgraph [8] Graph unions of cactus graphs: The four-vertex diamond graph formed by removing an edge from the complete graph K 4: Graph ...
In graph theory, a cycle decomposition is a decomposition (a partitioning of a graph's edges) into cycles. Every vertex in a graph that has a cycle decomposition must ...
A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph . Similar notions may be defined for directed graphs , where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices ...
Every graph has a cycle basis in which every cycle is an induced cycle. In a 3-vertex-connected graph, there always exists a basis consisting of peripheral cycles, cycles whose removal does not separate the remaining graph. [4] [5] In any graph other than one formed by adding one edge to a cycle, a peripheral cycle must be an induced cycle.
Steps of the cell cycle. The G 2-M checkpoint occurs between the G 2 and M phases. G2-M arrest. The G 2-M DNA damage checkpoint is an important cell cycle checkpoint in eukaryotic organisms that ensures that cells don't initiate mitosis until damaged or incompletely replicated DNA is sufficiently repaired.
Test whether adding the edge to the current forest would create a cycle. If not, add the edge to the forest, combining two trees into a single tree. At the termination of the algorithm, the forest forms a minimum spanning forest of the graph. If the graph is connected, the forest has a single component and forms a minimum spanning tree.
Cycle graph, a graph that consists of a single cycle; Chordal graph, a graph in which every induced cycle is a triangle; Directed acyclic graph, a directed graph with no directed cycles; Forest, a cycle-free graph; Line perfect graph, a graph in which every odd cycle is a triangle; Perfect graph, a graph with no induced cycles or their ...
A graph with an odd cycle transversal of size 2: removing the two blue bottom vertices leaves a bipartite graph. In graph theory, an odd cycle transversal of an undirected graph is a set of vertices of the graph that has a nonempty intersection with every odd cycle in the graph. Removing the vertices of an odd cycle transversal from a graph ...