Search Results - "Wenger, Paul S"

Colored Saturation Parameters for Rainbow Subgraphs by Barrus, Michael D., Ferrara, Michael, Vandenbussche, Jennifer, Wenger, Paul S.

“…Inspired by a 1987 result of Hanson and Toft [Edge‐colored saturated graphs, J Graph Theory 11 (1987), 191–196] and several recent results, we consider the…”
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Saturation Numbers in Tripartite Graphs by Sullivan, Eric, Wenger, Paul S.

“…Given graphs H and F, a subgraph G⊆H is an F‐saturated subgraph of H if F⊈G, but F⊆G+e for all e∈E(H)∖E(G). The saturation number of F in H, denoted sat (H,F),…”
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Planar Digraphs without Large Acyclic Sets by Knauer, Kolja, Valicov, Petru, Wenger, Paul S.

“…Given a directed graph, an acyclic set is a set of vertices inducing a directed subgraph with no directed cycle. In this note, we show that for all integers…”
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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs by Immel, Poppy, Wenger, Paul S.

“…A of a graph is a coloring of the vertices so that every nontrivial automorphism of maps some vertex to a vertex with a different color. The of is the minimum…”
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Uniquely Cycle‐Saturated Graphs by Wenger, Paul S., West, Douglas B.

“…Given a graph F, a graph G is uniquely F‐saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F. In…”
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On the sum necessary to ensure that a degree sequence is potentially H-graphic by Ferrara, Michael J., Lesaulnier, Timothy D., Moffatt, Casey K., Wenger, Paul S.

“…Given a graph H , a graphic sequence π is potentially H-graphic if there is some realization of π that contains H as a subgraph. In 1991, Erdős, Jacobson and…”
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List distinguishing parameters of trees by Ferrara, Michael, Gethner, Ellen, Hartke, Stephen G., Stolee, Derrick, Wenger, Paul S.

“…A coloring of the vertices of a graph G is said to be distinguishing provided no nontrivial automorphism of G preserves all of the vertex colors. The…”
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Fractional acquisition in graphs by Wenger, Paul S.

“…Let G be a vertex-weighted graph in which each vertex has weight 1. Given a vertex u with positive weight and a neighbor v whose weight is at least the weight…”
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A note on the saturation number of the family of k-connected graphs by Wenger, Paul S.

“…Given a family of graphs F, a graph G is F-saturated if no member of F is a subgraph of G, but for all e∈E(G¯), some member of F is a subgraph of G+e. The…”
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Unit Hypercube Visibility Numbers of Trees by Peterson, Eric, Wenger, Paul S.

“…A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their…”
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The Unit Bar Visibility Number of a Graph by Gaub, Emily, Rose, Michelle, Wenger, Paul

“…A $t$-unit-bar representation of a graph $G$ is an assignment of sets of at most $t$ horizontal unit-length segments in the plane to the vertices of $G$ so…”
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Saturation numbers for families of graph subdivisions by Ferrara, Michael, Jacobson, Michael, Milans, Kevin G., Tennenhouse, Craig, Wenger, Paul S.

“…For a family F of graphs, a graph G is F‐saturated if G contains no member of F as a subgraph, but for any edge uv in G¯, G+uv contains some member of F as a…”
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Uniquely C 4-Saturated Graphs by Cooper, Joshua, Lenz, John, LeSaulnier, Timothy D., Wenger, Paul S., West, Douglas B.

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Uniquely C ^sub 4^-Saturated Graphs by Cooper, Joshua, Lenz, John, Lesaulnier, Timothy D, Wenger, Paul S, West, Douglas B

“…For a fixed graph H, a graph G is uniquely H-saturated if G does not contain H, but the addition of any edge from G to G completes exactly one copy of H. Using…”
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Uniquely C sub(4)-Saturated Graphs by Cooper, Joshua, Lenz, John, LeSaulnier, Timothy D, Wenger, Paul S, West, Douglas B

“…For a fixed graph H, a graph G is uniquely H-saturated if G does not contain H, but the addition of any edge from G [macr] to G completes exactly one copy of…”
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Uniquely C4-Saturated Graphs by Cooper, Joshua, Lenz, John, LeSaulnier, Timothy D., Wenger, Paul S., West, Douglas B.

“…For a fixed graph H , a graph G is uniquely H-saturated if G does not contain H , but the addition of any edge from to G completes exactly one copy of H …”
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Unit Hypercube Visibility Numbers of Trees by Peterson, Eric, Wenger, Paul S

“…A visibility representation of a graph $G$ is an assignment of the vertices of $G$ to geometric objects such that vertices are adjacent if and only if their…”
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The List Distinguishing Number Equals the Distinguishing Number for Interval Graphs by Immel, Poppy, Wenger, Paul S

“…A \textit{distinguishing coloring} of a graph $G$ is a coloring of the vertices so that every nontrivial automorphism of $G$ maps some vertex to a vertex with…”
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Saturation numbers in tripartite graphs by Sullivan, Eric, Wenger, Paul S

“…Given graphs $H$ and $F$, a subgraph $G\subseteq H$ is an $F$-saturated subgraph of $H$ if $F\nsubseteq G$, but $F\subseteq G+e$ for all $e\in E(H)\setminus…”
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The Unit Acquisition Number of a Graph by Johnson, Frederick, Raleigh, Anna, Wenger, Paul S, West, Douglas B

“…Let $G$ be a graph with nonnegative integer weights. A {\it unit acquisition move} transfers one unit of weight from a vertex to a neighbor that has at least…”
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