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- Guantao Chen, Joan P. Hutchinson, Wiktor Piotrowski, Warren E. Shreve, Bing Wei
- Ars Comb.
- 2001

A given nonincreasing sequence D = (d1, d2, · · · , dn) is said to contain a (nonincreasing) repetition sequence D * = (di 1 , di 2 , · · · , di k) for some k ≤ n − 2 if all values of D − D * are distinct and for any di l ∈ D * there exists some dt ∈ D − D * such that di l = dt. For any pair of integers n and k with n ≥ k + 2, we investigate the existence… (More)

- Marvin D. Nelson, Kendall E. Nygard, John H. Griffin, Warren E. Shreve
- Computers & OR
- 1985

- Guantao Chen, Richard H. Schelp, Warren E. Shreve
- Eur. J. Comb.
- 1997

Consider the following two-person game on a graph G. Players I and II move alternatively to color a yet uncolored vertex of G properly using a pre-specified set of colors. Furthermore , Player II can only use the colors that have been used , unless he is forced to use a new color to guarantee that the graph is colored properly. The game ends when some… (More)

- Xiaotao Cai, Warren E. Shreve
- Discrete Mathematics
- 2001

For any natural number k, a graph G is said to be pancyclic mod k if it contains a cycle of every length modulo k. In this paper, we show that every K 1,4-free graph G with minimum degree δ(G) ≥ k + 3 is pancyclic mod k and every claw-free graph G with δ(G) ≥ k + 1 is pancyclic mod k, which confirms Thomassen's conjecture [8] for claw-free graphs.

- Guantao Chen, Wiktor Piotrowski, Warren E. Shreve
- Journal of Graph Theory
- 1996

- Guantao Chen, Jenö Lehel, Michael S. Jacobson, Warren E. Shreve
- Journal of Graph Theory
- 1998

- WARREN E. SHREVE
- 2010

A result of Ladas; Lakshmikantham, and Papadakis [1] concerning oscillation caused by lag in linear first order retarded argument differential equations is generalized to the sublinear case. Examples showing that such generalization to the superlinear case is impossible are given. 0. Introduction. It is known ([1], for example) that (A) g e C(R, R), g(t) <… (More)

- Guantao Chen, Warren E. Shreve, Bing Wei
- Journal of Graph Theory
- 2006

- Xiaotao Cai, Warren E. Shreve
- Ars Comb.
- 2001

For two integers k(> 0) and s(≥ 0), a cycle of length l is called an (s mod k)-cycle if l ≡ s mod k. In this paper, the following conjecture of Chen, Dean, and Shreve [5] is proved: Every 2-connected graph with at least six vertices and minimum degree at least three contains a (2 mod 4)-cycle. 1 INTRODUCTION We use [2] for our notation and terminology. Our… (More)

- Guantao Chen, Ralph J. Faudree, Warren E. Shreve
- Ars Comb.
- 2001

In this paper, we investigate the sufficient conditions for a graph to contain a cycle (path) C such that G − V (C) is a disjoint union of cliques. In particular, sufficient conditions involving degree sum and neighborhood union are obtained.