Abstract
The Subgraph polynomial fo a graph pair (G, H), where H⫅G, is defined. By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial.
Highlights
By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial
We will say that an edge e of G is incorporated in G, if it is distinguished in some way and required to belong to every cover K that we consider
By applying the theorem recursively, we can obtain an algorithm for finding subgraph polynomials of graph pairs
Summary
By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. A GENERALIZATION OF THE DICHROMATIC POLYNOMIAL OF A GRAPH The Subgraph polynomial fo a graph pair (G,H), where H G, is defined. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial.
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