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Full-Text Articles in Physical Sciences and Mathematics
On Graphs With Proper Connection Number 2, Jill Faudree, Leah Berman, Glenn Chappell, Chris Hartman, John Gimbel, Gordon Williams
On Graphs With Proper Connection Number 2, Jill Faudree, Leah Berman, Glenn Chappell, Chris Hartman, John Gimbel, Gordon Williams
Theory and Applications of Graphs
An edge-colored graph is properly connected if for every pair of vertices u and v there exists a properly colored uv-path (i.e. a uv-path in which no two consecutive edges have the same color). The proper connection number of a connected graph G, denoted pc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is properly connected. An edge-colored graph is flexibly connected if for every pair of vertices u and v there exist two properly colored paths between them, say P and Q, such …
The Color Number Of Cubic Graphs Having A Spanning Tree With A Bounded Number Of Leaves, Analen A. Malnegro, Gina A. Malacas, Kenta Ozeki
The Color Number Of Cubic Graphs Having A Spanning Tree With A Bounded Number Of Leaves, Analen A. Malnegro, Gina A. Malacas, Kenta Ozeki
Theory and Applications of Graphs
The color number c(G) of a cubic graphG is the minimum cardinality of a color class of a proper 4-edge-coloring of G. It is well-known that every cubic graph G satisfies c(G) = 0 if G
Embedding Factorizations, Anna Johnsen
Embedding Factorizations, Anna Johnsen
Theses and Dissertations
Let $V$ be a set of $n$ vertices for some $n\in\mathbb{N}$ and let $E$ be a collection of $h$-subsets of $V$. Then $\mathscr G = (V,E)$ is an $h$-unifrom hypergraph and we refer to $V$ as its vertex set and to $E$ as its edge set. We say that $\mathscr G$ is complete and denote it by $K_n^h$ if every $h$-subset of $V$ is contained in $E$. If every edge in $E$ is repeated $\lambda$ times, we say $G$ is $\lambda$-fold. Specifically, $\lambda K_n^h$ is the complete $\lambda$-fold $n$-vertex $h$-uniform hypergraph with an edge set containing $\lambda$ copies of every …