Introducing edge-biregular maps
نویسندگان
چکیده
Abstract We introduce the concept of alternate-edge-colourings for maps and study highly symmetric examples such maps. Edge-biregular type ( k , l ) occur as smooth normal quotients a particular index two subgroup $$T_{k,l}$$ T k , l full triangle group describing regular plane )-tessellations. The resulting colour-preserving automorphism groups can be generated by four involutions. explore special cases when usual generators are not distinct involutions, with constructions relating these to fully classify edge-biregular supporting surface has non-negative Euler characteristic, on arbitrary surfaces is isomorphic dihedral group.
منابع مشابه
On one-sided interval edge colorings of biregular bipartite graphs
A proper edge t-coloring of a graphG is a coloring of edges of G with colors 1, 2, . . . , t such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex x is called a spectrum of x. Any nonempty subset of consecutive integers is called an interval. A proper edge t-coloring of a graph G is interval in the vertex x if the spec...
متن کاملIntroducing Rigor in Concept Maps
Although concept maps have been found to be effective in science education research, these are critiqued for being informal due to informal usage of relation and attribute names thereby resulting in ambiguity. Refined concept mapping, a development over the regular concept mapping is an approach towards introducing rigor and parsimony in representing knowledge. The method proposed suggests to s...
متن کاملSome results on interval edge colorings of (α, β)-biregular bipartite graphs
A bipartite graph G is called (α, β)-biregular if all vertices in one part of G have the degree α and all vertices in the other part have the degree β. An edge coloring of a graph G with colors 1, 2, 3, . . . , t is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored ...
متن کاملProper path-factors and interval edge-coloring of (3, 4)-biregular bigraphs
An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3, 4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring usin...
متن کاملOn Interval Edge Colorings of Biregular Bipartite Graphs With Small Vertex Degrees
A proper edge coloring of a graph with colors 1, 2, 3, . . . is called an interval coloring if the colors on the edges incident to each vertex form an interval of integers. A bipartite graph is (a, b)-biregular if every vertex in one part has degree a and every vertex in the other part has degree b. It has been conjectured that all such graphs have interval colorings. We prove that all (3, 6)-b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2021
ISSN: ['0925-9899', '1572-9192']
DOI: https://doi.org/10.1007/s10801-021-01097-9