[PDF] Top 20 Perfect Matchings in Edge-Transitive Graphs

... To compute ( ), we have to compute ( ) and ( \{ , }). ( ) = 2 and to compute ( \ , ), we omit two vertices of , resulting in, two remained vertices. If these vertices are neighbors, there will be one perfect ... See full document

... an edge-coloured bipartite graph the colour classes of which induce perfect matchings of size n + ...the matchings are disjoint, but not necessarily ... See full document

... bounded and locally o(n/ log 2 n)-bounded has (1 − o(1))n edge-disjoint rainbow perfect matchings. This is on one hand stronger than Theorem 1.2 since it also works for locally bounded colorings, but ... See full document

... For matchings, there are a large number of results related to matching ...the graphs that have perfect matchings and Edmonds [20] provided an efficient algorithm to find such a matching in ... See full document

... Γ- perfect if β(H) = Γ(H), for every induced subgraph H of ...Γ-perfect graphs in terms of some family of forbidden induced subgraphs, and show that the class of Γ-perfect graphs is a ... See full document

... Circle graphs. Circle graphs are those whose vertices can be rep- resented as chords on a circle in such a way that two nodes in the graph are adjacent if and only if the corresponding chords ...circle ... See full document

... bipartite graphs, it is easier to search for augmenting paths using of bread-first ...general graphs were ...non-bipartite graphs by “shrinking” ... See full document

... From an assumption perspective, the existing constructions of iO [GGH + 13b, BR14, BGK + 13, AB15, Zim15, AJ15, BV15, GLSW14] are instantiated based on multi-linear graded encodings [GGH13a, CLT13, CLT15] thus falling ... See full document

... and edge set ...a perfect dominating set of G if |N (v) ∩ S| = 1 for each v ∊ V- ...trivial perfect dominating set consisting of all vertices in ...the perfect dominating set of G is the ... See full document

... Now as a onsequen e of Theorem 2.3, in the proof of Theorem 1.3, we may assume that is a square-free graph that ontains a proper wheel or a para hute... rst prove the theorem when ontain[r] ... See full document

... This is the peer reviewed version of the following article: Hertz A, Lozin V, Ries B, Zamaraev V, de Werra D. Dominating induced matchings in graphs containing no long claw. J Graph Theory. 2017. ... See full document

... Sequential join is a graph operation that is introduced by Harary 1181. Graphs obtained by using this operation, represent a communication network construction [2]. Consider for three or more disjoint ... See full document

... An edge cover in a graph G = (V, E) is a subset W ⊆ E of edges such that each vertex v ∈ V is the endpoint of at least one edge in W .... Edge covers and matchings are related in graph theory ... See full document

... V = q . Also, the underlying set V is assumed to be finite and σ can be chosen in any manner so as to satisfy the definition of a fuzzy graph in all the examples and all these properties are satisfied for all fuzzy ... See full document

... This proof is inspired by previous renormalization procedures that were developed for Z d , see for instance [41]. Here we adapt them to work on more general classes of graphs. Although Theorem 1.9 is not the ... See full document

... two graphs is defined in [3] and there have been some results on the corona of two graphs ...two graphs G and H ; denoted by G H ; is the graph obtained by taking one copy of G of order n and n ... See full document

... in graphs is a historical problem in ...of perfect codes in Johnson ...Johnson graphs, including J (6, 3), J(7, 3), J(8, 3), J(8, 4), and J (v, 3) (v odd) (see [1, 2, ... See full document

... – perfect degree support graph (k – pds graph) if for any vertex v in G, the ratio of its support and its degree is the constant ...lds graphs and k – pds graphs in various product graphs have ... See full document

... Proof: By definition, no two vertices corresponding edges in Ne(G) are adjacent and no two vertices corresponding to open edge neighborhood sets in Ne(G) are adjacent.. Thus Ne(G) h[r] ... See full document

... ommon graphs. A graph H is ommon if a quasirandom graph minimizes the sum of densities of H and the omplement of H . An old theorem of Goodman [12℄ says that the omplete graph K 3 is ommon. The onjeture of Erd®s ... See full document