Even [a,b]-factors in graphs
Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a,b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.
Even and odd tournament matrices with minimum rank over finite fields.
Even bonds of prescribed directed parity.
Even circuits of prescribed clockwise parity.
Even factor of bridgeless graphs containing two specified edges
An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Let be a bridgeless simple graph with minimum degree at least . Jackson and Yoshimoto (2007) showed that has an even factor containing two arbitrary prescribed edges. They also proved that has an even factor in which each component has order at least four. Moreover, Xiong, Lu and Han (2009) showed that for each pair of edges and of , there is an even factor containing and in which each...
Every connected acyclic digraph of height 1 is neighbourhood-realizable
Every finite lattice can be embedded in the lattice of all equivalences over a finite set (Preliminary communication)
Every forest can be obtained from a minimal block.
Every graph is an induced isopart of a circulant
Evolution in random environment and structural instability.
Evolutionary families of sets.
Exact -step domination in graphs
For a vertex in a graph , the set consists of those vertices of whose distance from is 2. If a graph contains a set of vertices such that the sets , , form a partition of , then is called a -step domination graph. We describe -step domination graphs possessing some prescribed property. In addition, all -step domination paths and cycles are determined.
Exact double domination in graphs
In a graph a vertex is said to dominate itself and all its neighbours. A doubly dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. A doubly dominating set is exact if every vertex of G is dominated exactly twice. We prove that the existence of an exact doubly dominating set is an NP-complete problem. We show that if an exact double dominating set exists then all such sets have the same size, and we establish bounds on this size. We give a constructive...
Exact Expectation and Variance of Minimal Basis of Random Matroids
We formulate and prove a formula to compute the expected value of the minimal random basis of an arbitrary finite matroid whose elements are assigned weights which are independent and uniformly distributed on the interval [0, 1]. This method yields an exact formula in terms of the Tutte polynomial. We give a simple formula to find the minimal random basis of the projective geometry PG(r − 1, q).
Exactly solvable and unsolvable shortest network problems in 3D-space.
Examples of Λ(4) sets E and a graph structure in E x E
Existence and nonexistence of universal graphs
Existence of graphs with sub exponential transitions probability decay and applications
In this paper, we recall the existence of graphs with bounded valency such that the simple random walk has a return probability at time at the origin of order for fixed and with Følner function . This result was proved by Erschler (see [4], [3]); we give a more detailed proof of this construction in the appendix. In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on...
Existence of -factors in powers of connected graphs
Existence of perfect matchings in a plane bipartite graph
We give a necessary and sufficient condition for the existence of perfect matchings in a plane bipartite graph in terms of elementary edge-cut, which extends the result for the existence of perfect matchings in a hexagonal system given in the paper of F. Zhang, R. Chen and X. Guo (1985).