The Relative Maximum Genus of a Graph

The Maximum Number of Edges in a Strongly Multiplicative Graph

Matchings, Cycle Bases, and the Maximum Genus of a Graph

We study the interplay between the maximum genus of a graph and bases of its cycle space via the corresponding intersection graph. Our main results show that the matching number of the intersection graph is independent of the basis precisely when the graph is upper-embeddable, and completely describe the range of matching numbers when the graph is not upper-embeddable. Particular attention is p...

A Nebeský-Type Characterization for Relative Maximum Genus

This paper concerns the maximum genus orientable surface upon which a given graph cellularly embeds. Classical theorems of Xuong and Nebesk y give exact values for the maximum genus. The former is suited to constructing embeddings while the latter is suited to forbidding embeddings of larger genus. However, using either theorem alone requires an exhaustive search to establish the exact value. H...

On the Maximum Number of Dominating Classes in Graph Coloring

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

the maximum number of edges in a strongly multiplicative graph

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