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Full-Text Articles in Physical Sciences and Mathematics
Gallai-Ramsey And Vertex Proper Connection Numbers, Emily C. Chizmar
Gallai-Ramsey And Vertex Proper Connection Numbers, Emily C. Chizmar
Honors College Theses
Given a complete graph G, we consider two separate scenarios. First, we consider the minimum number N such that every coloring of G using exactly k colors contains either a rainbow triangle or a monochromatic star on t vertices. This number is known for small cases and generalized for larger cases for a fixed k. Second, we introduce the vertex proper connection number of a graph and provide a relationship to the chromatic number of minimally connected subgraphs. Also a notion of total proper connection is introduced and a question is asked about a possible relationship between the total proper …
Graphs Obtained From Collections Of Blocks, Colton Magnant, Pouria Salehi Nowbandegani, Hua Wang
Graphs Obtained From Collections Of Blocks, Colton Magnant, Pouria Salehi Nowbandegani, Hua Wang
Department of Mathematical Sciences Faculty Publications
Given a collection of d-dimensional rectangular solids called blocks, no two of which sharing interior points, construct a block graph by adding a vertex for each block and an edge if the faces of the two corresponding blocks intersect nontrivially. It is known that if d ≥ 3, such block graphs can have arbitrarily large chromatic number. We prove that the chromatic number can be bounded with only a mild restriction on the sizes of the blocks. We also show that block graphs of block configurations arising from partitions of d-dimensional hypercubes into sub-hypercubes are at least d-connected. Bounds on …