On Vizing's theorem, adjacency lemma and fan argument generalized to multigraphs

An adjacency lemma for critical multigraphs

In edge colouring it is often useful to have information about the degree distribution of the neighbours of a given vertex. For example, the well known Vizing’s Adjacency Lemma provides a useful lower bound on the number of vertices of maximum degree adjacent to a given one in a critical graph. We consider an extension of this problem, where we seek information on vertices at distance two from ...

On a lemma of Ky Fan

The object of this note is to give two applications of an intersection lemma of Ky Fan. First it is used to obtain a variational property of a strongly continuous function on a weakly compact convex subset of a normed space. In the second half we apply the lemma to obtain a direct proof of a result on the extension of monotone sets in topological linear spaces. It was established separately by ...

An Adjacency Constraint on Argument Selection

Fan-KKM Theorem in Minimal Vector Spaces and its Applications

In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM typetheorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.

The fan theorem