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9.916  Articles
1 of 993 pages  |  10  records  |  more records»
The Alon-Tarsi number AT(G) of a graph G is the least k for which there is an orientation D of G with max outdegree k - 1 such that the number of spanning Eulerian subgraphs of G w... see more

A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f - 2 of which are of size d and the remaining two are of sizes d1, d2, both different from d. Such a graph is ca... see more

The notion of the matrix Jacobson graph was introduced in 2019. Let R be a commutative ring and J(R) be the Jacobson radical of ring R. The matrix Jacobson graph of ring R size m × n, denoted ??(R)m × n, is def... see more

A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek,... see more

Modeling a road network as a planar graph seems very natural. However, in studying continuum limits of such networks it is useful to take {\em routes} rather than {\em edges} as primitives. This article is intended to introduce the relevant (dis... see more

The g-girth-thickness ?(g, G) of a graph G is the smallest number of planar subgraphs of girth at least g whose union is G. In this paper, we calculate the 4-girth-thickness ?(4, G) of the complete m-partite graph G when each part has an even number of ve... see more

The Hanani–Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generali... see more

A zonal labeling of a plane graph G is an assignment of the two nonzero elements of the ring Z3 of integers modulo 3 to the vertices of G such that the sum of the labels of the vertices on the boundary of each regio... see more

Sazdanovic and Yip (2018) defined a categorification of Stanley’s chromatic symmetric function called the chromatic symmetric homology, given by a suitable family of representations of the symmetric group. In this paper we prove that, as co... see more

1 of 993 pages  |  10  records  |  more records»