Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree ∆ ≥ M(g) is (∆+1)-colorable. The conjecture… (More)

Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the chromatic number of the square of every planar graph of girth at least g and maximum degree ∆ ≥ M(g) is ∆ + 1.… (More)

Motivated by a conjecture of Wang and Lih, we show that every planar graph of girth at least 7 and maximum degree ∆ ≥ 190 + 2⌈p/q⌉ has an L(p, q)-labeling of span at most 2p+q∆−2. Since the optimal… (More)

The Shortest Cycle Cover Conjecture of Alon and Tarsi asserts that the edges of every bridgeless graph with m edges can be covered by cycles of total length at most 7m/5 = 1.400m. We show that every… (More)

Motivated by previous results on distance constrained labelings and coloring of squares of K4-minor free graphs, we show that for every p ≥ q ≥ 1, there exists ∆0 such that every K4-minor free graph… (More)

The Shortest Cycle Cover Conjecture of Alon and Tarsi asserts that the edges of every bridgeless graph with m edges can be covered by cycles of total length at most 7m/5 = 1.400m. We show that every… (More)

Lih, Wang and Zhu [Discrete Math. 269 (2003), 303–309] proved that the chromatic number of the square of a K4-minor free graph with maximum degree ∆ is bounded by ⌊3∆/2⌋+1 if ∆ ≥ 4, and is at most… (More)