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Search Results: 1 - 10 of 150744 matches for " Douglas B. West "
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Line digraphs and coreflexive vertex sets
Xinming Liu,Douglas B. West
Mathematics , 1998,
Abstract: The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection digraph from a given digraph.
Coloring of Trees with Minimum Sum of Colors
Tao Jiang,Douglas B. West
Mathematics , 1999,
Abstract: The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength is the minimum number of colors needed to achieve the chromatic sum. We construct for each positive integer k a tree with strength k that has maximum degree only 2k-2. The result is best possible.
A note on generalized chromatic number and generalized girth
Béla Bollobás,Douglas B. West
Mathematics , 1998,
Abstract: Erd\H{o}s proved that there are graphs with arbitrarily large girth and chromatic number. We study the extension of this for generalized chromatic numbers.
A Guide to the Discharging Method
Daniel W. Cranston,Douglas B. West
Mathematics , 2013,
Abstract: We provide a "how-to" guide to the use and application of the Discharging Method. Our aim is not to exhaustively survey results that have been proved by this technique, but rather to demystify the technique and facilitate its wider use. Along the way, we present some new proofs and new problems.
Classes of 3-regular graphs that are (7, 2)-edge-choosable
Daniel W. Cranston,Douglas B. West
Mathematics , 2008,
Abstract: A graph is (7, 2)-edge-choosable if, for every assignment of lists of size 7 to the edges, it is possible to choose two colors for each edge from its list so that no color is chosen for two incident edges. We show that every 3-edge-colorable graph is (7, 2)-edge-choosable and also that many non-3-edge-colorable 3-regular graphs are (7, 2)-edge-choosable.
Multiple vertex coverings by specified induced subgraphs
Zoltan Furedi,Dhruv Mubayi,Douglas B. West
Mathematics , 1999,
Abstract: Given graphs H_1,...,H_k, we study the minimum order of a graph G such that for each i, the induced copies of H_i in G cover V(G). We prove a general upper bound of twice the sum of the numbers m_i, where m_i is one less than the order of H_i. When k=2 and one graph is an independent set of size n, we determine the optimum within a constant. When k=2 and the graphs are a star and an independent set, we determine the answer exactly.
Uniquely cycle-saturated graphs
Paul S. Wenger,Douglas B. West
Mathematics , 2015,
Abstract: Given a graph $F$, a graph $G$ is {\it 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 this paper we study uniquely $C_t$-saturated graphs. We prove the following: (1) a graph is uniquely $C_5$-saturated if and only if it is a friendship graph. (2) There are no uniquely $C_6$-saturated graphs or uniquely $C_7$-saturated graphs. (3) For $t\ge6$, there are only finitely many uniquely $C_t$-saturated graphs (we conjecture that in fact there are none).
The bricklayer problem and the Strong Cycle Lemma
Hunter S. Snevily,Douglas B. West
Mathematics , 1998,
Abstract: We introduce a combinatorial enumeration problem that is solved using generalized Catalan numbers. We also study generalizations of the Cycle Lemma beyond the computation of the generalized Catalan numbers.
A short proof that ``proper = unit''
Kenneth P. Bogart,Douglas B. West
Mathematics , 1998,
Abstract: A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.
Star-factors of tournaments
Guantao Chen,Xiaoyun Lu,Douglas B. West
Mathematics , 1998,
Abstract: Let S_m denote the m-vertex simple digraph formed by m-1 edges with a common tail. Let f(m) denote the minimum n such that every n-vertex tournament has a spanning subgraph consisting of n/m disjoint copies of S_m. We prove that m lg m - m lg lg m <= f(m) <= 4m^2 - 6m for sufficiently large m.
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